How to use ODE 45 to generate a SIR model

function Math462hw2Q6parte

alpha=1.99;

beta=1;

gamma=1/7;

S=0.99;

I=0.01;

R=0.1;

%tstart=0;

%tend=100;

y=[S,I,R];

tspan=0:1:100;

[t,soln]=ode45(@(t,y)dotfunctions,tspan,y);

%plot function

plot(t,soln);

xlabel('time');

ylabel('value');

title('double pendulum');

function ddt=dotfunctions(~,sir)

S=sir(1);

I=sir(2);

R=sir(3);

Sdot=-beta*S*I+alpha*R;

Idot=beta*S*I-gamma*I;

Rdot=gamma*I-alpha*R;

ddt=[S,I,R,Sdot,Idot,Rdot];

end

end

The above is my code and MATLAB keeps saying the line with the function ode45 is not right. I do not know where the mistakes are. Could someone help me figure it out? THANKS!

Answer 1

[Alan Stevens]

Like so:

alpha=1.99;
beta=1;
gamma=1/7;
S=0.99;
I=0.01;
R=0.1;
%tstart=0;
%tend=100;
y=[S,I,R];
tspan=0:1:100;
[t,soln]=ode45(@(t,y)dotfunctions(t,y,alpha,beta,gamma),tspan,y);  % Pass constants to function
%plot function
plot(t,soln);
xlabel('time');
ylabel('value');
title('double pendulum');
    function ddt=dotfunctions(~,sir,alpha,beta,gamma)
        S=sir(1);
        I=sir(2);
        R=sir(3);
        
        Sdot=-beta*S*I+alpha*R;
        Idot=beta*S*I-gamma*I;
        Rdot=gamma*I-alpha*R;
        ddt=[Sdot;Idot;Rdot];  % Just the gradients.  Must be column vector
    end

[Zhukun Wang]

Gotcha, that works. Thanks so much!

[darova]