Eq points of a set of ODEs with parametric values

Hi! I'm quite new to Matlab and I have a couple of questions:

I need to find the eq. points of a system of 3 ODEs, with some parametric coefficient (about which I know the value). In particular, the idea is to define the ODEs with all the parameters, set one of the parameters to zero, find the the eq points in a parametric shape, and then subtitute their value to get the numerical solution of the eq. points. That's because I need to evaluate different cases with different parameters, and I'd like to avoid to write the code for each case.

Here's what I wrote, can someone help me, please?

PS: I know that the equilibrium points can be defined by setting the first derivative = 0, but I need to keep the ODEs in their original shape for later steps.

clc;
clear;
close all;

% Definition of ODE system

syms s(t) e(t) i(t)               
syms mu betaz q sigma gamma             % Parameters

ode1 = diff(s) == mu - betaz * (1-q) * s * i - mu * s;
ode2 = diff(e) == betaz * (1-q) * s * i - (sigma + mu) * e;
ode3 = diff(i) == sigma * e - (gamma + mu) * i;

q = 0;

diff(s) == 0;
diff(e) == 0;
diff(i) == 0;

rz = (sigma * betaz) / ((mu + sigma) * (mu + gamma));

% Case 1

mu = 0.5;
betaz = 0.9;
sigma = 0.95;
gamma = 1/5;

eq1 = solve(ode1);
eq2 = solve(ode1);
eq3 = solve(ode1);
rz;

Answer 1

[Rijuta]

Hi Mattia,

I understand that you are trying to implement your code for multiple cases without duplicating the code.

This can be done by storing the parameter values for each case in a data structure like a cell array and then loop through each case to solve the ODEs, in the same way as you have done for a single case.

I hope the above information helps in implementing the code for multiple cases.