% 1. if a line starts with % - this line is a comment and will not be executed
% by matlab
% 2. if a line ends with ; - the result of the execution of this line will not 
% appear on the screen. try to omit ; after one of the lines below and see what happens


%%%%%%%%%%
% MAIN PART
%%%%%%%%%%

%set up parameter values

dt=0.5; %days
alpha=0.3; % 1/day

p_dt=alpha*dt;

% define initial condition:
I0=100;

% define time points (vector t) in which we want to compute our solutions
% t is from 0 to 15 with 0.5 day increments
% if you omit ; here you will see all components of  the vector t
t=0:0.5:15;

%Now compute the solutions:

%continuous:

I_Cont=I0*exp(-alpha*t);
%notice that I_Cont will be the same length as t. the operation will be
%performed to each component of the vector t

%discrete:

% convert t to discrete points
n=0:length(t)-1;
% when the increment is 1 it can be omiited

%solution:
I_Disc=I0*(1-p_dt).^n;

%%%%%%%%%%%
% plotting
%%%%%%%%%%

%open figure
figure(1)

%type 'help plot' in command window to find out how this command works
% you can do the same with any other command. also helpwin will open a
% whole help window and help help will give you some basic menus
plot(t,I_Cont)

% prevent future drawings on the same graph from erasing the existing one 
hold on

plot(t,I_Disc,'o')

%label axis
xlabel('Time, days')
ylabel('Number of infected individuals')

%%%%%%%%%%%%%%%
%PART II
%%%%%%%%%%%%%%
%do the same for different alpha and plot in red

alpha=0.2;

p_dt=alpha*dt;

%continuous:
I_Cont=I0*exp(-alpha*t);

%discrete:
I_Disc=I0*(1-p_dt).^n;

plot(t,I_Cont,'r')

plot(t,I_Disc,'or')