From 6dd60a83c98f28feb3a5f9e7046c38fe79f7e101 Mon Sep 17 00:00:00 2001
From: Paul CACHEUX <paulcacheux@gmail.com>
Date: Wed, 23 May 2018 16:33:12 +0200
Subject: [PATCH] Ajout vaccination modulaire, et differents step (waiting)
pour l'infection
---
SRI_matlab/main.m | 56 +++++++++++++++++++++++++++++++-------------
SRI_matlab/options.m | 1 -
SRI_matlab/step.m | 27 ++++++++++++++++-----
3 files changed, 61 insertions(+), 23 deletions(-)
diff --git a/SRI_matlab/main.m b/SRI_matlab/main.m
index 9064c7e..4d7bbf1 100644
--- a/SRI_matlab/main.m
+++ b/SRI_matlab/main.m
@@ -1,24 +1,26 @@
clear figure
+N = 180;
+
S = 990;
-I = 50;
+I = 10;
R = 0;
-n_pop = S + I + R;
-input = [S, I, R];
+% input = [S, I, R];
+input = build_input(S, I, R, 12);
coeffs = options;
-coeffs.InfectionRate = 0.09;
-coeffs.ImmunisationRate = 0.005;
-coeffs.ImmunisationLossRate = 0.001;
-coeffs.VaccinationRate = 0.02;
-coeffs.DeathRate = 0.04;
-coeffs.NaturalDeathRate = 0.002;
-coeffs.NatalityRate = 0.003;
-
-N = 1000;
+coeffs.InfectionRate = 0.6;
+coeffs.ImmunisationRate = 0.04;
+coeffs.ImmunisationLossRate = 2.7e-4;
+coeffs.DeathRate = 1.3e-3;
+coeffs.NaturalDeathRate = 2e-5;
+coeffs.NatalityRate = 5e-5;
+% VaccinationRate = build_vacc_rate(0, 2.4e-4, 50, N);
+VaccinationRate = build_vacc_rate(0, 0, 50, N);
Slist = zeros(1, N);
+Wlist = zeros(1, N);
Ilist = zeros(1, N);
Rlist = zeros(1, N);
@@ -28,7 +30,8 @@ for i=t
Slist(i) = input(1);
Ilist(i) = input(2);
Rlist(i) = input(3);
- input = step(input, coeffs);
+ Wlist(i) = sum(input(4:length(input)));
+ input = step(input, coeffs, VaccinationRate(i));
end
% figure
@@ -37,10 +40,31 @@ end
% plot(t, Ilist);
% plot(t, Rlist);
% plot(t, Dlist);
-area([Slist.', Ilist.', Rlist.']);
+area([Slist.', Wlist.', Ilist.', Rlist.']);
-legend('Susceptible', 'Infected', 'Immunized');
+legend('Susceptible', 'Waiting', 'Infected', 'Immunized');
title('Evolution of virus in population');
xlabel('Time');
ylabel('Population');
-axis([1, N, 0, inf]);
\ No newline at end of file
+axis([1, N, 0, inf]);
+
+% utility functions
+
+function input=build_input(S, I, R, Waiting)
+ input(1) = S;
+ input(2) = I;
+ input(3) = R;
+ for i = 1:Waiting
+ input(3+i) = 0;
+ end
+end
+
+function vacc_rate=build_vacc_rate(start_rate, end_rate, change_step, N)
+ vacc_rate = zeros(1, N);
+ for i=1:change_step
+ vacc_rate(i) = start_rate;
+ end
+ for i=change_step+1:N
+ vacc_rate(i) = end_rate;
+ end
+end
\ No newline at end of file
diff --git a/SRI_matlab/options.m b/SRI_matlab/options.m
index 3dfd8dc..76d8ad7 100644
--- a/SRI_matlab/options.m
+++ b/SRI_matlab/options.m
@@ -3,7 +3,6 @@ classdef options
InfectionRate
ImmunisationRate
ImmunisationLossRate
- VaccinationRate
DeathRate
NaturalDeathRate
NatalityRate
diff --git a/SRI_matlab/step.m b/SRI_matlab/step.m
index 8e1f987..55f2f96 100644
--- a/SRI_matlab/step.m
+++ b/SRI_matlab/step.m
@@ -1,13 +1,28 @@
-function res = step(X, options)
+function res = step(X, options, VaccinationRate)
S = X(1);
I = X(2);
R = X(3);
-N = S + I + R;
+N = sum(X);
-dS = -options.InfectionRate * S * I/N - options.VaccinationRate * S + options.ImmunisationLossRate * R + options.NatalityRate * N - options.NaturalDeathRate * S;
-dI = options.InfectionRate * S * I/N - options.ImmunisationRate * I - options.DeathRate * I;
-dR = options.ImmunisationRate * I + options.VaccinationRate * S - options.ImmunisationLossRate * R - options.NaturalDeathRate * R;
+new_waiting = zeros(1, length(X) - 3);
+for i=5:length(X)
+ new_waiting(i - 3) = X(i - 1) * (1 - options.NaturalDeathRate);
+end
-res = [max(S + dS, 0), max(I + dI, 0), max(R + dR, 0)];
+if length(X) > 3
+ infecter = sum(X(4:length(X)) + I);
+ new_waiting(1) = options.InfectionRate * S * infecter/N;
+ dS = -options.InfectionRate * S * infecter/N;
+ dI = X(length(X));
+else
+ dS = -options.InfectionRate * S * I/N;
+ dI = options.InfectionRate * S * I/N;
+end
+
+dS = dS - VaccinationRate * S + options.ImmunisationLossRate * R + options.NatalityRate * N - options.NaturalDeathRate * S;
+dI = dI - options.ImmunisationRate * I - options.DeathRate * I;
+dR = options.ImmunisationRate * I + VaccinationRate * S - options.ImmunisationLossRate * R - options.NaturalDeathRate * R;
+
+res = [max(S + dS, 0), max(I + dI, 0), max(R + dR, 0), new_waiting];
end
\ No newline at end of file
--
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