SIR Simulation

%% SIR Simulation
% Susceptible, Infected, and Resistant Simulation
% Defines model parameters, time vector, and preallocates
% vectors for the three populations, and defines initial conditions

clc, clear
Beta = 0.3;
mu = 0.1;
dt = 1;
t = 0:1:600;
S = zeros(1, 601);
I = zeros(1, 601);
R = zeros(1, 601);
BetaT = zeros(1, 601);

BetaT(1:end) = Beta;
N = 8000000;
R(1) = 0;
I(1) = 1;
S(1) = N-I(1);
stop_length = length(t)-1;

for i = 1:stop_length
    S(i+1) = ((-BetaT(i)*I(i)*S(i))/N)*dt+S(i);
    I(i+1) = (((BetaT(i)*I(i)*S(i))/N)-(mu*I(i)))*dt+I(i);
    R(i+1) = (mu*I(i))*dt+R(i);
end

hold on
plot(t, S)
plot(t, I)
plot(t, R)
legend('Susceptible Counts', 'Infected Counts', 'Resistant Counts', 'Location', 'best')
ylabel('Counts')
xlabel('Time(days)')
title('SIR Counts vs. Days')