%% SIR Model Matlab
%% Init

% timestep
dt=0.001;
% iterations
iter=20000;

% initialize vectors
x=zeros(iter,1); %predator
y=zeros(iter,1); %prey


x(1)=10; y(1)=10; % starting point

a = 1.5; % alpha:
b = 1; % beta: 
g = 3; % gamma: 
d = 1; % delta: 

figure()

%% Iteration
for i=2:iter
    
    dx=x(i-1)*(a-b*y(i-1));
    dy=-y(i-1)*(g-d*x(i-1));
    
    x(i)=x(i-1)+dt*dx;
    y(i)=y(i-1)+dt*dy;
    
    % plot ([x y])
    %xlabel('time');
    %ylabel('pop');
    %legend('predator','prey');
    %grid on
    
    
    % to see in real-time
    % pause(0.1)
    
end

plot ([x y])