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main.m
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main.m
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clear all
close all
%% Download COVID19 data from italian Protezione Civile github account
t1 = datetime(2020,03,24,8,0,0); % First day
t2 = datetime(2021,9,14,8,0,0); % Last day
tInterval = t1:t2;
NInterval = numel(tInterval); % Number of days
covidTable = cell(NInterval, 1);
for i=1:NInterval
date_str = datestr(tInterval(i), 'yyyymmdd');
fname = downloadItalianCovidData(date_str, './data');
covidTable{i} = readtable(fname, 'ReadVariableNames',true);
end
% Extract the relevant data
hospitalized = zeros(NInterval, 1);
quarantined = zeros(NInterval, 1);
recovered = zeros(NInterval, 1);
deceased = zeros(NInterval, 1);
for i=1:NInterval
ct = covidTable{i};
for row=1:21 % Italian regions
hospitalized(i) = hospitalized(i) + ct.totale_ospedalizzati(row);
quarantined(i) = quarantined(i) + ct.isolamento_domiciliare(row);
recovered(i) = recovered(i) + ct.dimessi_guariti(row);
deceased(i) = deceased(i) + ct.deceduti(row);
end
end
Idata = hospitalized + quarantined;
Rdata = recovered;
Ddata = deceased;
Tw = 30; % Length of a time window
W = floor(numel(Idata)/Tw); % Number of time windows
%% General parameters
M = 60244639; % Italian population size
%% Parameters setup (IGM)
par_obj_IGM = setParameter(); % Create an empty parameter object
par_obj_IGM = setParameter(par_obj_IGM, 'S0', 'tinvar', 59*1e6, 0.98*M, M);
par_obj_IGM = setParameter(par_obj_IGM, 'x0', 'tinvar', 0.41, 0.1, 0.9);
par_obj_IGM = setParameter(par_obj_IGM, 'beta0', 'tinvar', 0.5, 0.1, 0.7);
par_obj_IGM = setParameter(par_obj_IGM, 'gamma', 'const', 1/14);
par_obj_IGM = setParameter(par_obj_IGM, 'sigmaC0', 'tinvar', 4.22, 1e-2, 10);
par_obj_IGM = setParameter(par_obj_IGM, 'sigmaN0', 'tinvar', -4.2, -10, -1e-2);
par_obj_IGM = setParameter(par_obj_IGM, 'alpha', 'tvar', 0.03, 1e-4, 0.2833);
par_obj_IGM = setParameter(par_obj_IGM, 'tau', 'const', 0.166);
par_obj_IGM = setParameter(par_obj_IGM, 'omega', 'tvar', 0.019, 1e-4, 1/7);
par_obj_IGM = setParameter(par_obj_IGM, 'zeta', 'tvar', 0.01, 1e-4, 0.3);
par_obj_IGM = setParameter(par_obj_IGM, 'e', 'tvar', 0.75, 0.05, 0.95);
par_obj_IGM = setParameter(par_obj_IGM, 'a', 'tvar', 87370, 1, 1e6);
[theta0_IGM, lb_IGM, ub_IGM] = getParameter(par_obj_IGM, W); % % Build up ic, lb and ub vectors for the optimization problem
%% Parameters setup (IM)
par_obj_IM = setParameter(); % Create an empty parameter object
par_obj_IM = setParameter(par_obj_IM, 'S0', 'tinvar', 59*1e6, 0.98*M, M);
par_obj_IM = setParameter(par_obj_IM, 'x0', 'const', 0); % n.a.
par_obj_IM = setParameter(par_obj_IM, 'beta0', 'tvar', 0.5, 0.1, 0.7); % n.a.
par_obj_IM = setParameter(par_obj_IM, 'gamma', 'const', 1/14);
par_obj_IM = setParameter(par_obj_IM, 'sigmaC0', 'const', 0); % n.a.
par_obj_IM = setParameter(par_obj_IM, 'sigmaN0', 'const', 0); % n.a.
par_obj_IM = setParameter(par_obj_IM, 'alpha', 'tvar', 0.03, 1e-4, 0.2833);
par_obj_IM = setParameter(par_obj_IM, 'tau', 'const', 0.166);
par_obj_IM = setParameter(par_obj_IM, 'omega', 'tvar', 0.019, 1e-4, 1/7);
par_obj_IM = setParameter(par_obj_IM, 'zeta', 'tvar', 0.01, 1e-4, 0.3);
par_obj_IM = setParameter(par_obj_IM, 'e', 'const', 0); % n.a.
par_obj_IM = setParameter(par_obj_IM, 'a', 'const', 0); % n.a.
[theta0_IM, lb_IM, ub_IM] = getParameter(par_obj_IM, W); % Build up ic, lb and ub vectors for the optimization problem
%% Estimate
thetaOptim_IGM = estimate(W, Tw, Idata, Rdata, Ddata, lb_IGM, ub_IGM, theta0_IGM, par_obj_IGM, M);
thetaOptim_IM = estimate(W, Tw, Idata, Rdata, Ddata, lb_IM, ub_IM, theta0_IM, par_obj_IM, M);
%% Simulate
tBreaks = zeros(W, 1);
tBreaks(1) = Tw-1;
for i=2:W
tBreaks(i) = tBreaks(i-1) + Tw;
end
[S_IGM, U_IGM, I_IGM, R_IGM, D_IGM, x_IGM] = simode(thetaOptim_IGM, ...
Idata, ...
Rdata, ...
Ddata, ...
M, ...
tBreaks, ...
par_obj_IGM);
[S_IM, U_IM, I_IM, R_IM, D_IM, x_IM] = simode(thetaOptim_IM, ...
Idata, ...
Rdata, ...
Ddata, ...
M, ...
tBreaks, ...
par_obj_IM);
%% Plot
colorlist = lines(7);
figure
subplot(3,1,1)
hold on
plot(0:tBreaks(end), Idata(1:tBreaks(end)+1), 'o', 'LineWidth', 2, 'Color', colorlist(3,:), 'MarkerSize', 5);
plot(0:tBreaks(end), I_IM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), I_IGM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('Real data', 'Sim. IM', 'Sim. IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$I(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(3,1,2)
hold on
plot(0:tBreaks(end), Rdata(1:tBreaks(end)+1), 'o', 'LineWidth', 2, 'Color', colorlist(3,:), 'MarkerSize', 5);
plot(0:tBreaks(end), R_IM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), R_IGM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('Real data', 'Sim. IM', 'Sim. IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$R(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(3,1,3)
hold on
plot(0:tBreaks(end), Ddata(1:tBreaks(end)+1), 'o', 'LineWidth', 2, 'Color', colorlist(3,:), 'MarkerSize', 5);
plot(0:tBreaks(end), D_IM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), D_IGM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('Real data', 'Sim. IM', 'Sim. IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$D(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
%% Plot parameters
beta0_IGM = [];
gamma_IGM = [];
tau_IGM = [];
omega_IGM = [];
zeta_IGM = [];
sigmaC0_IGM = [];
sigmaN0_IGM = [];
alpha_IGM = [];
e_IGM = [];
a_IGM = [];
beta0_IM = [];
gamma_IM = [];
tau_IM = [];
omega_IM = [];
zeta_IM = [];
sigmaC0_IM = [];
sigmaN0_IM = [];
alpha_IM = [];
e_IM = [];
a_IM = [];
for i=1:W % Extract the estimated parameter values
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'beta0', i);
beta0_IGM = [beta0_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'gamma', i);
gamma_IGM = [gamma_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'tau', i);
tau_IGM = [tau_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'omega', i);
omega_IGM = [omega_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'zeta', i);
zeta_IGM = [zeta_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'sigmaC0', i);
sigmaC0_IGM = [sigmaC0_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'sigmaN0', i);
sigmaN0_IGM = [sigmaN0_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'alpha', i);
alpha_IGM = [alpha_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'e', i);
e_IGM = [e_IGM; val*ones(Tw, 1)];
val = getParameter(par_obj_IGM, W, thetaOptim_IGM, 'a', i);
a_IGM = [a_IGM; val*ones(Tw, 1)];
%% IM
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'beta0', i);
beta0_IM = [beta0_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'gamma', i);
gamma_IM = [gamma_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'tau', i);
tau_IM = [tau_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'omega', i);
omega_IM = [omega_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'zeta', i);
zeta_IM = [zeta_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'sigmaC0', i);
sigmaC0_IM = [sigmaC0_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'sigmaN0', i);
sigmaN0_IM = [sigmaN0_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'alpha', i);
alpha_IM = [alpha_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'e', i);
e_IM = [e_IM; val*ones(Tw, 1)];
val = getParameter(par_obj_IM, W, thetaOptim_IM, 'a', i);
a_IM = [a_IM; val*ones(Tw, 1)];
end
%% alpha, omega, zeta
figure
subplot(1,3,1)
hold on
plot(0:tBreaks(end), alpha_IM, 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), alpha_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('IM', 'IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$\alpha(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(1,3,2)
hold on
plot(0:tBreaks(end), omega_IM, 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), omega_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('IM', 'IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$\omega(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(1,3,3)
hold on
plot(0:tBreaks(end), zeta_IM, 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), zeta_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('IM', 'IGM', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
ylabel('$\zeta(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
%% a, G(I,D) - e, x, ex - beta
figure
subplot(1,3,1)
hold on
yyaxis left
plot(0:tBreaks(end), a_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
set(gca, 'YColor', colorlist(1,:));
yyaxis right
G_IGM = (I_IGM+D_IGM-a_IGM)/M;
plot(0:tBreaks(end), G_IGM, 'LineWidth', 2, 'Color', colorlist(4,:));
plot(0:tBreaks(end), 0*G_IGM, '--', 'LineWidth', 2, 'Color', [0 0 0]);
set(gca, 'YColor', colorlist(4,:));
xlim([0 539])
legend('$a$', '$G(I,D)$', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(1,3,2)
hold on
plot(0:tBreaks(end), e_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
plot(0:tBreaks(end), x_IGM, 'LineWidth', 2, 'Color', colorlist(4,:));
plot(0:tBreaks(end), e_IGM.*x_IGM, 'LineWidth', 2, 'Color', colorlist(5,:));
xlim([0 539])
legend('$e$', '$x$', '$ex$', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
subplot(1,3,3)
hold on
plot(0:tBreaks(end), beta0_IM, 'LineWidth', 2, 'Color', colorlist(2,:));
plot(0:tBreaks(end), beta0_IGM.*(1-e_IGM.*x_IGM), 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539])
legend('$\beta$ (IM)', '$\beta$ (IGM)', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
return
%% U
figure
% subplot(1,2,1)
hold on
yyaxis left
% plot(0:tBreaks(end), res_nox.Y(1:tBreaks(end)+1), 'LineWidth', 2);
plot(0:tBreaks(end), U_IGM(1:tBreaks(end)+1), 'LineWidth', 2, 'Color', colorlist(1,:));
ylabel('$U(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'YColor', colorlist(1,:));
yyaxis right
data_yex = 100*U_IGM(1:tBreaks(end)+1)./(U_IGM(1:tBreaks(end)+1)+I_IGM(1:tBreaks(end)+1));
% data_yex_2 = 100*mypos(res_yex.Y(1:tBreaks(end)+1))./mypos(res_yex.C(1:tBreaks(end)+1));
plot(0:tBreaks(end), data_yex, 'LineWidth', 2, 'Color', colorlist(4,:));
% plot(0:tBreaks(end), data_yex_2, 'LineWidth', 2);
ylabel('$U(t)$ (\%)', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'YColor', colorlist(4,:));
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlim([0 539])
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
%% R0
RO_IM = beta0_IM./(gamma_IM+tau_IM);
RO_IGM = beta0_IGM.*(1-e_IGM.*x_IGM)./(gamma_IGM+tau_IGM);
RO_IGM_0 = beta0_IGM./(gamma_IGM+tau_IGM);
RO_IGM_ott = beta0_IGM.*(1-e_IGM)./(gamma_IGM+tau_IGM);
R0_diff_data = zeros(numel(Idata)-1, 1);
for i=1:numel(Idata)-1
R0_diff_data(i) = 1 + ((Idata(i+1)-Idata(i))/Idata(i))/(1/14 + 0.166);
end
k1p_est = M*(1-1/RO_IGM_0(1));
fprintf('k1 primo: %.4f\n', k1p_est);
% R0_diff_data(448) = (R0_diff_data(449) + R0_diff_data(447))/2;
figure; %('Position', [285 401 1270 270])
% subplot(1,3,1)
hold on
x_patch = 0:tBreaks(end);
x_patch = [0:tBreaks(end), x_patch(end:-1:1)];
y_patch_1 = [RO_IGM_0; RO_IGM(end:-1:1)];
hp1 = patch(x_patch, y_patch_1, 'c');
hp1.FaceColor = colorlist(4,:);
hp1.FaceAlpha = 0.3;
y_patch_2 = [RO_IGM; RO_IGM_ott(end:-1:1)];
hp2 = patch(x_patch, y_patch_2, 'g');
hp2.FaceColor = colorlist(5,:);
hp2.FaceAlpha = 0.3;
h = zeros(4, 1);
h(1) = plot(1:tBreaks(end), R0_diff_data, 'o', 'LineWidth', 2, 'Color', colorlist(3,:), 'MarkerSize', 3);
h(2) = plot(0:tBreaks(end), RO_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
h(3) = plot(0:tBreaks(end), RO_IGM_0, 'LineWidth', 2, 'Color', colorlist(4,:));
h(4) = plot(0:tBreaks(end), RO_IGM_ott, 'LineWidth', 2, 'Color', colorlist(5,:));
plot(0:tBreaks(end), 1+0*RO_IGM_ott, '--', 'LineWidth', 2, 'Color', [0 0 0 ]);
%
% yyaxis right
% h(5) = plot(2:tBreaks(end), diff(R0_diff_data), 'r', 'LineWidth', 2);
% set(gca, 'YColor', 'r')
% plot(0:tBreaks(end), alpha_IGM, 'LineWidth', 2, 'Color', colorlist(1,:));
xlim([0 539]) %tBreaks(end)])
legend(h, 'Real data', '$\mathcal{R}(t)$ (IGM)', '$\mathcal{R}_0$ (IGM)', '$\underline{\mathcal{R}}$ (IGM)', 'Interpreter', 'latex', 'FontSize', 12, 'Location', 'northwest')
% ylabel('$\alpha(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 12)
xlabel('$t$ (days)' , 'Interpreter', 'latex', 'FontSize', 12)
yl = ylim;
ylim([0.2 1.5])
%%
figure
hs = scatter(e_IGM(1:30:540), I_IGM(1:30:540), 200, 1:18, 'filled');
hold on
hs2 = scatter(e_IGM(1:30:510), I_IGM(31:30:540), 200, 1:17, 'filled');
hs2.Marker = 'd';
for i=1:18
text(e_IGM(1+(i-1)*30), I_IGM(1+(i-1)*30), num2str(i));
end
% AA = zeros(17);
% for i=1:16
% AA(i,i+1) = 1;
% end
% G = digraph(AA);
figure
% subplot(1,2,1)
myranges_I = {7, [5 6], [1 2 3 4 8:17]};
myranges_D = {[6 7], [], [1:5 8:17]};
for j=1:3
if (j < 3)
subplot(6,1,j)
else
subplot(6,1,[3 4 5 6])
end
i_tmp = zeros(18, 1);
d_tmp = zeros(18, 1);
% i_diff = diff(I_IGM(1:540));
d_diff = diff(D_IGM(1:540));
for i=1:18
if (i<18)
d_tmp(i) = max(d_diff(1+(i-1)*30:30*i));
i_tmp(i) = max(I_IGM(1+(i-1)*30:30*i));
else
d_tmp(i) = max(d_diff(1+(i-1)*30:30*i-1));
i_tmp(i) = max(I_IGM(1+(i-1)*30:30*i-1));
end
end
y =100*(i_tmp(2:18)-i_tmp(1:17))./i_tmp(1:17);
y(12) = -5;
x = e_IGM(1:30:510);
hold on
plot([0, 1], 0*[0 1], 'k--')
hs = scatter(x,y,300,1:17,'filled');
hs.MarkerFaceColor = colorlist(3,:);
hs.MarkerFaceAlpha = 0.7;
for i=myranges_I{j} %1:17
htxt = text(x(i)+0.02, y(i)+0.02, num2str(i));
htxt.FontSize = 12;
end
% ylabel('$I(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 16)
y =100*(d_tmp(2:18)-d_tmp(1:17))./d_tmp(1:17);
y(12) = -5;
x = e_IGM(1:30:510);
hold on
% plot([min(x), max(x)], 0*[min(x), max(x)], 'k--')
hs2 = scatter(x,y,300,1:17,'filled');
hs2.MarkerFaceColor = colorlist(4,:);
hs2.MarkerFaceAlpha = 0.7;
for i=myranges_D{j} %1:17
htxt = text(x(i)-0.02, y(i)-0.02, num2str(i));
htxt.FontSize = 12;
end
% ylabel('$\dot{D}(t)$', 'Interpreter', 'latex', 'FontSize', 12)
set(gca, 'TickLabelInterpreter', 'latex', 'fontsize', 16)
if (j == 1)
ylim([450 560])
set(gca,'XTick', [], 'YTick', 500)
elseif (j==2)
ylim([180 205])
set(gca,'XTick', [], 'YTick', 195)
else
ylim([-95 35]);
xlabel('$e$' , 'Interpreter', 'latex', 'FontSize', 16)
ylabel('$\Delta \%$' , 'Interpreter', 'latex', 'FontSize', 16)
legend([hs hs2], '$I$', '$D$', 'Interpreter', 'latex', 'FontSize', 16)
end
xlim([0 1])
end
return
% % % REGIONI - TRIMESTRI
I_IGM_tmp_end = zeros(6, 1);
E_IGM_tmp_end = zeros(6, 1);
A_IGM_tmp_end = zeros(6, 1);
for i=1:6
I_IGM_tmp_end(i) = max(I_IGM(1+(i-1)*90:i*90));
E_IGM_tmp_end(i) = mean(e_IGM(1+(i-1)*90:i*90));
A_IGM_tmp_end(i) = mean(a_IGM(1+(i-1)*90:i*90));
end
figure
hold on
scatter(E_IGM_tmp_end, A_IGM_tmp_end, 200, I_IGM_tmp_end, 'filled')
for i=1:6
ht = text(E_IGM_tmp_end(i), A_IGM_tmp_end(i), sprintf('%d', i));
set(ht, 'FontSize', 16)
end
aut = autumn;
aut = aut(end:-1:1,:);
colormap(aut)
colorbar
% % % REGIONI - PRED UN MESE AVANTI PER DIVERSI e ed a
e_grid = 0.1:0.1:0.9;
a_grid = linspace(1e5, 4e5, 9);
e_pred = zeros(numel(e_grid)*numel(a_grid), 1);
a_pred = zeros(numel(e_grid)*numel(a_grid), 1);
I_pred = zeros(numel(e_grid)*numel(a_grid), 1);
% Idata, ...
% Rdata, ...
% Ddata, ...
tBreaks = zeros(W-1, 1);
tBreaks(1) = Tw-1;
for i=2:W-1
tBreaks(i) = tBreaks(i-1) + Tw;
end
h = 0;
for i=1:numel(e_grid)
for j=1:numel(a_grid)
[i j]
thetaOptim_pred_IGM = [thetaOptim_IGM; thetaOptim_IGM(end-(n_tvar_IM-1):end)]; %thetaOptim_IGM(end-(n_tvar_IM-1):end)];
thetaOptim_pred_IGM(7+4+(19-1)*5) = e_grid(i);
thetaOptim_pred_IGM(7+5+(19-1)*5) = a_grid(j);
%
% thetaOptim_pred_IGM(7+4+(20-1)*5) = e_grid(i);
% thetaOptim_pred_IGM(7+5+(20-1)*5) = a_grid(j);
[S_IGM_tmp, U_IGM_tmp, I_IGM_tmp, R_IGM_tmp, D_IGM_tmp, x_IGM_tmp] = simode(thetaOptim_pred_IGM, ...
Idata(1), ...
Rdata(1), ...
Ddata(1), ...
M, ...
tBreaks, ...
par_obj_IGM);
h = h + 1;
I_pred(h) = I_IGM_tmp(end);
e_pred(h) = e_grid(i);
a_pred(h) = a_grid(j);
end
end
scatter(e_pred, a_pred, 100, I_pred, 'Marker', 'd')
figure
scatter(e_pred, a_pred, 100, I_pred, 'filled')
aut = autumn;
aut = aut(end:-1:1,:);
colormap(aut)
colorbar