MATLAB: Solve system of differential equations using Euler forward and ode45

differential equationseulerode45sir model

I have a basic SIR model which is described by three differential equations:
and I want to solve these using Euler forward and ode45. I have never worked with these types of problems before but from research I have found that for Euler forward I should use the equations:
But all the examples I have seen using this are given initial values for the different parameters, which I haven't. So I don't even know where to start. I would appreciate if someone could push me in the right direction of how to solve this. Thank you!

Best Answer

When using Euler forward, you start with
S(1) = s0; % initial value of S
I(1) = i0; % initial value of I
R(1) = r0; % initial value of R
and then run for loop using the equations in your question
N = % total number of time steps
dT = % length of each time step
for i = 2:N
    S(i) = S(i-1) + % equation for Sn in question
    I(i) = I(i-1) + % equation for In in question
    R(i) = R(i-1) + % equation for Rn in question
end
t = 0:dT:(N-1)*dT;
plot(t, S, t, I, t, R)
See these example of how Euler method can be written in MATLAB
https://www.mathworks.com/matlabcentral/fileexchange/45664-euler-method
https://www.mathworks.com/matlabcentral/fileexchange/72522-euler-method
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