Solving Differential equations of a modified SIR model

Hi, I want to solve a system of differential equations for a modified SIR model but being stocked and don't know how to go about it. I need someone to assist me with the code. The equations are shown below: a =0, V=0.4, Beta= 0.2, gamma= 0.01

Answer 1

[Sam Chak]

Hi @ELUFISAN PAUL TOMILOLA

The simulation shows some results, although I didn't check/compare your equations with the standard models in

https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology

Note that ϵ is not given. If , then and converge very fast.

function Demo_SIR

close all;

clear;

clc;

Tspan = [0 1e3]; % simulation time

y0 = [1000; 500; 5; 5; 0; 0]; % initial values

[t, y] = ode45(@SIR, Tspan, y0);

plot(t, y, 'linewidth', 1.5)

grid on

xlabel('Time')

ylabel('Individual')

legend({'$S_{1}$', '$S_{2}$', '$I_{1}$', '$I_{2}$', '$R_{1}$', '$R_{2}$'}, 'Interpreter', 'latex', 'location', 'best')

title('Responses of the SIR model')

end

function dydt = SIR(t, y)

dydt = zeros(6,1);

alpha = 0;

beta = 0.00002;

gamma = 0.01;

epsilon = 0.125;

V = 0.4;

S1 = y(1);

S2 = y(2);

I1 = y(3);

I2 = y(4);

R1 = y(5);

R2 = y(6);

dydt(1) = - beta*S1*((1 - epsilon)*(1 + alpha/V)*I1 + (1 - epsilon)*I2);

dydt(2) = - beta*S2*(I1 + I2);

dydt(3) = - (gamma*I1) - (- beta*S1*((1 - epsilon)*(1 + alpha/V)*I1 + (1 - epsilon)*I2));

dydt(4) = - (gamma*I2) - (- beta*S2*(I1 + I2));

dydt(5) = gamma*I1;

dydt(6) = gamma*I2;

end

Result: