% This file should be saved as sir.m
% This code complements that of Example_SIR_Model.m to be run in matlab.

function sir =sir(t,N) 
% sir is the series of ordinary differential equations
% works in conjuction with Example_SIR_Model.m
 
%Parameters
a = .01; % Infection rate.  This parameter could be broken into the contact 
% rate and the probalility of infection given contact.
b = .1;  % Recovery rate
 
%Differential Equations for each population 
sir(1) =-a*N(1)*N(2);  % Susceptible
sir(2) = a*N(1)*N(2)-b*N(2);  % Infected
sir(3) = b*N(2); % Recovered
 
 
sir = [sir(1) sir(2) sir(3)]';
 
 
 
% SI Model
% If individuals don't recover (i.e. they immediately become susceptible 
% after clearing the infection), then the model is an SI model.
 
% Then, replace the above sir(1-3) with the below equations:
%       sir(1) = -a*y(1)*y(2) + b*y(2);  % Susceptible
%       sir(2) = a*y(1)*y(2)-b*y(2);   % Infected
 
% If you switch this out make sure to change N0 to have only 2 values
% instead of 3 and update the figure legend.