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ITA.m
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%%
clc
clear all
close all
% GET DATA FROM SCRIPT
% add folders to path
addpath('./data/');
addpath('./models/');
addpath('./results/overview');
addpath('./results/january/ITA');
addpath('./results/october/ITA');
addpath('./models/SIR');
addpath('./models/SEIR');
addpath('./models/SEIIR');
addpath('./models/SEIIRHD');
%retrieve the data structs
[data, dates] = getData;
sizes = size(dates);
size_data = sizes(2);
N = 60.*10^6;
t0 = find(dates=="08-Oct-2020");
tf = find(dates=="23-Nov-2020");
%% PLOT OVERVIEW DATA
% da rifare prima della consegna
plot_data(data, dates, N, 1, size_data, "./results/overview/OverviewPlot.png");
%% PLOT OCTOBER DATA
close all
plot_data(data, dates(t0:tf), N, t0, tf, "./results/october/ITA/octoberPlot.png");
%% FITTING SIR MODEL
% [S, I, R]
beta0 = 0.962/N;
gamma0 = 0.37;
% adimensional SIR model for fitting
% We divide every variable by N
% s = S/N, e= E/N etc.
% [s, i, r]
% s' = -(beta*N)*(S/N)*(I/N) = -(beta*N)*s*i
% i' = (beta*N)*(S/N)*(I/N) - (gamma)*(I/N) = (beta*N)*s*i - gamma*i
% r' = gamma*(I/N) = gamma*i
I = cast((data.totale_positivi), 'double');
R = cast((data.dimessi_guariti), 'double');
S = N-I;
X_SIR = [S, I, R];
X_ad_SIR = [S, I, R]/N;
% initial conditions
I0 = I(t0);
R0 = R(t0);
S0 = N-I0;
X0_ad_SIR = [S0 I0 R0]/N;
beta0 = beta0*N;
p0_SIR = [beta0, gamma0];
p_SIR = fit_SIR(X_ad_SIR, X0_ad_SIR, p0_SIR, t0, tf);
fprintf("--- SIR FITTING DONE --- \n");
fprintf("beta: %f, gamma: %f \n", p_SIR(1), p_SIR(2));
%% R0 SIR
F = p_SIR(1);
V = p_SIR(2);
G = F*inv(V);
R0 = eigs(G,1);
fprintf("R0: %f \n", R0);
%% PLOT SIR
close all
tp = [7,14, 21];
plot_SIR(X_SIR, X0_ad_SIR, N, p_SIR, dates, t0, tf, tp,"./results/october/ITA/SIR_fitting.png");
%% FITTING SEIR MODEL
% [S, E, I, R]
E = 0.3*(I);
S = N-I-E-R;
X = [S, E, I, R];
X_SEIR = [S, E, I, R];
X_ad_SEIR = [S, E, I, R]/N;
% adimensional SEIR model for fitting
% We divide every variable by N
% s = S/N, e= E/N etc.
% [s, e, i, r]
% s' = -(beta*N)*(S/N)*(I/N) = -(beta*N)*s*i
% e' = (beta*N)*(S/N)*(I/N) - alpha*(E/N) = (beta*N)*s*i - alpha*e
% i' = alpha*(E/N)-gamma*(I/N) = alpha*e-gamma*i
% r' = gamma*(I/N) = gamma*i
% initial conditions
E0 = E(t0);
I0 = I(t0);
R0 = R(t0);
S0 = N-E0-I0-R0;
X0_ad_SEIR = [S0 E0 I0 R0]/N;
S0 = N;
tau = 5.1; %paper SEIR
alpha0=1/tau;
% initial beta and gamma are taken from the previous simulation results
beta0 = p_SIR(1);
gamma0 = p_SIR(2);
p0_SEIR = [beta0, alpha0, gamma0];
p_SEIR = fit_SEIR(X_ad_SEIR, X0_ad_SEIR, p0_SEIR, t0, tf);
fprintf("--- SEIR FITTING DONE --- \n");
fprintf("beta: %f, alpha: %f, gamma: %f \n", p_SEIR(1), p_SEIR(2), p_SEIR(3));
%% R0 SEIR
F = [0 p_SEIR(1); 0 0];
V = [p_SEIR(2) 0; -p_SEIR(2) p_SEIR(3)];
G = F*inv(V);
R0 = eigs(G,1);
fprintf("R0: %f\n", R0);
%% PLOT SEIR
close all
tp = [7,14, 21];
plot_SEIR(X_SEIR, X0_ad_SEIR, N, p_SEIR, dates, t0, tf, tp,"./results/october/ITA/SEIR_fitting.png");
%% FITTING SEIIR MODEL
S = N-E-I-R;
%f presa dal paper
f0 = 0.4264;
I_a = (1-f0)*I;
I_s = f0*I;
X_SEIIR = [S, E, I_a, I_s, R];
X_ad_SEIIR = [S, E, I_a, I_s, R]/N;
% initial conditions
E0 = E(t0);
I_a0 = I_a(t0);
I_s0 = I_s(t0);
R0 = R(t0);
X0_ad_SEIIR = [S0 E0 I_a0 I_s0 R0]/N;
alpha0 = p_SEIR(2);
gamma0 = p_SEIR(3);
beta_a0 = 0.05;
beta_s0 = 0.675281;
p0_SEIIR = [f0, alpha0, gamma0, beta_a0, beta_s0];
p_SEIIR = fit_SEIIR(X_ad_SEIIR, X0_ad_SEIIR, p0_SEIIR, t0, tf);
fprintf("--- SEIIR FITTING DONE --- \n");
fprintf("f0: %f, alpha: %f, gamma: %f, beta_a: %f, beta_s: %f\n"...
, p_SEIIR(1), p_SEIIR(2), p_SEIIR(3), p_SEIIR(4), p_SEIIR(5));
%% PLOT SEIIR
close all
tp = [7,14, 21];
plot_SEIIR(X_SEIIR, X0_ad_SEIIR, N, p_SEIIR, dates, t0, tf, tp,...
"./results/october/ITA/SEIIR_fitting.png");
%% FITTING SEIIRHD MODEL
S = N-E-I-R;
R = cast(data.dimessi_guariti, 'double');
H = cast(data.totale_ospedalizzati, 'double');
D = cast(data.deceduti, 'double');
X_SEIIRHD = [S, E, I_a, I_s, H, R, D];
X_ad_SEIIRHD = [S, E, I_a, I_s, H, R, D]/N;
% initial conditions
E0 = E(t0);
I_a0 = I_a(t0);
I_s0 = I_s(t0);
H0 = H(t0);
R0 = R(t0);
D0 = D(t0);
X0_ad_SEIIRHD = [S0 E0 I_a0 I_s0 H0 R0 D0]/N;
f0 = p_SEIIR(1);
alpha0 = p_SEIIR(2);
gamma0 = p_SEIIR(3);
beta_a0 = p_SEIIR(4);
beta_s0 = p_SEIIR(5);
nu_s0 = 0.08;
mu0 = 0.0204;
p0_SEIIRHD = [f0, alpha0, gamma0, beta_a0, beta_s0, nu_s0, mu0];
p_SEIIRHD = fit_SEIIRHD(X_ad_SEIIRHD, X0_ad_SEIIRHD, p0_SEIIRHD, t0, tf);
fprintf("--- SEIIRHD FITTING DONE --- \n");
fprintf("f0: %f, alpha: %f, gamma: %f, \n beta_a: %f, beta_s: %f \n nu_s0: %f, mu0: %f \n"...
, p_SEIIRHD(1), p_SEIIRHD(2), p_SEIIRHD(3), ...
p_SEIIRHD(4), p_SEIIRHD(5), p_SEIIRHD(6),...
p_SEIIRHD(7));
%% RO SEIIRHD
F = [0 p_SEIIRHD(4) p_SEIIRHD(5); 0 0 0; 0 0 0];
V = [p_SEIIRHD(2) 0 0; ...
((p_SEIIRHD(1)-1)* p_SEIIRHD(2)) 0 p_SEIIRHD(3);
(-(p_SEIIRHD(2)*p_SEIIRHD(1))) (p_SEIIRHD(3) + p_SEIIRHD(6) + p_SEIIRHD(7)) 0];
G = F*inv(V);
R0 = eigs(G,1);
fprintf("R0: %f\n", R0);
%% PLOT SEIIRHD
close all
tp = [7,14, 21];
plot_SEIIRHD(X_SEIIRHD, X0_ad_SEIIRHD, N, p_SEIIRHD, dates, t0, tf, tp,...
"./results/october/ITA/SEIIRHD_fitting.png");
%% COMPUTE ERRORS
close all
tp = [60];
plot_SEIIRHD(X_SEIIRHD, X0_ad_SEIIRHD, N, p_SEIIRHD, dates, t0, tf, tp, ...
"./results/october/ITA/trailSEIIRHD.png");