Matlab functions of functions

So I am writing a function to compute the following equations for an SIR model:

So here's my code:

    function xdot = sir(t, params)
    global h r q;

    xdot = zeros(3,1);
    SH = params(1);
    IH = params(2);
    RH = params(3);

    xdot(1) = -h*SH + r*IH + gamma(h,t)*RH; % dSh
    xdot(2) = h*SH - r*IH - q*IH; %dIh
    xdot(3) = q*IH - gamma(h,t)*RH; %dRh

    end

And then I would call this function like so:

    global h r q;
    h = 1;
    r = 2;
    q = 3;
    params(1) = 1;
    params(2) = 2;
    params(3) = 3;
    [t x] = ode45('sir',[0:0.01:30],params);

But I just don't understand how to write the gamma function component inside of sir.m. What I mean is the gamma(h,tau) portion that is a part of the original equation. How exactly would I write this inside the function file sir.m?

Answer 1

[Walter Roberson]

That is not Gamma, that is Incomplete Gamma. See http://www.mathworks.com/help/matlab/ref/gammainc.html

[Adin]

So what exactly does using gammainc do? Sorry I'm new to matlab so I don't really know too much yet.

[Walter Roberson]

If I read your code correctly, where you have

gamma(h,t)

substitute

gammainc(t, h)

I notice you initialize your h to 1. When you follow through the defining formula for incomplete gamma, the t^(a-1) part will become t^0 so that term will vanish, leaving you with an integral from 0 to x of exp(-t) . The integral of exp(-t) is -exp(-t) so for that case gammainc(t,1) is (1 - exp(-t))