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I am trying to write a program on matlab using ode45 to solve the following equations:

S'=-bSZ-sS

Z'=bSZ+gR-aSZ

R'=sS+aSZ-gR

These are all derivatives with respect to t, differential equations.

a, b, a and g are all constants.

I realise I need to have two m files, one which defines the functions, and one which calls that and uses ode45. The code for my first m file is:

function Yout = program1(S,Z,R);

global beta gamma alpha sigma;

% set the parmeter values

tend = 10;

S0 = 500;

I0 = 1;

b=0.0095;

g=0.0001;

a= 0.005;

s=0.0001;

Sdot=(-b)*S*Z-(gg*S);

Zdot=(b*S*Z)+(g*R)-(a*S*Z);

Rdot=(s*S)+(a*S*Z)-(g*R);

udot = [Sdot; Zdot; Rdot];

I'm not sure if that is suitable, and I also need help writing the second m file. I need to plot Z and R on the same plot, vs t. I am really stuck, I have been working for hours, looking at examples, trying different combinations. MATLAB is most definitely not my strong point.

Thanks for the help!