siroutput.asv

%% This function takes three inputs
% x - a set of parameters
% t - the number of time-steps you wish to simulate
% data - actual data that you are attempting to fit

function f = siroutput(x,t,data)

% set up transmission constants
k_infections = x(1);
k_fatality = x(2);
k_recover = x(3);

% set up initial conditions
ic_susc = x(4);
ic_inf = x(5);
ic_rec = x(6);
ic_fatality = x(7);

% Set up SIRD within-population transmission matrix
A = [(1-k_infections)   0           0 0; 
        k_infections        (1-k_recover-k_fatality)           0 0;
        0                   k_recover   1 0;
        0                   k_fatality   0 1];
B = zeros(4,1);

% Set up the vector of initial conditions
x0 = [ic_susc, ic_inf, ic_rec, ic_fatality];

% simulate the SIRD model for t time-steps
sys_sir_base = ss(A,B,eye(4),zeros(4,1),1)
y = lsim(sys_sir_base,zeros(t,1),linspace(0,t-1,t),x0);

% return a "cost".  This is the quantitity that you want your model to
% minimize.  Basically, this should encapsulate the difference between your
% modeled data and the true data. Norms and distances will be useful here.
% Hint: This is a central part of this case study!  choices here will have
% a big impact!
%stl = data(data{:, 5} == 2, :);


%population = ic_susc-stl{:,4};
population = 1-data(:, 2);
casesModel = y(:, 2) + y(:, 3) + y(:, 4);

%1: Suscpetible, 2: infected, 3: 

% f =sum( (population-y(:, 1)).^2+ (casesModel-stl{:, 3}).^2 +(stl{:, 4}-y(:, 2)).^2);
f =sum( (population-y(:, 1)-y(:, 1)).^2+ (casesModel-data(:, 1)).^2 +(data(:, 2)-y(:, 2)).^2);
end