How to solve SIR model with ode45?

S'(t)=-λ(t)S(t) S(0)=So

Ι'(t)=λ(t)S(t)-γ(t) I(0)=Io

R'(t)=γ(t)I(t) R(0)=Ro

λ(t)=cx/N(t)*I(t)

γ(t)=1/τ

Answer 1

[Pavan Guntha]

You can refer to the following code:

[t,dYdt] = odeOut;

function [t,dYdt] = odeOut
% time dependent window
tRange  = linspace(0, 10, 100);         % Change the limits as per your requirement
Y0      = [S0; I0; R0];                 % initial conditions
yT      = 1/T;                          % Considering T to be a constant.
lambdaT = cx./(N(tRange).*I(tRange));   % N, I are to be defined

[t,dYdt] = ode45(@odefunc, tRange, Y0);
    function dYdt = odefunc(t,y)
        lambdaT_t = interp1(tRange,lambdaT,t);
        dSdt = -lambdaT_t*y(1);
        dIdt = lambdaT_t*y(2) - yT;
        dRdt = yT*y(3);
        dYdt = [dSdt; dIdt; dRdt];
    end
end

You can refer to the documentation of interp1 for more details about its usage.