function sir = sir_simulation ( m, n, a, k, tau, t_max )
%*****************************************************************************80
%
%% sir_simulation() simulates an SIR model of disease transmission.
%
% Discussion:
%
% We assume that a hospital ward comprises an array of M by N beds.
%
% The status of each patient is recorded as an integer in an array A.
%
% Susceptible patients, with a status of 0, have never had the disease.
%
% Infected patients, with a positive status between 1 and K, have
% had the disease for A(I,J) days.
%
% Recovered patients, with a status of -1, have had the disease for K
% days, are no longer infected, and cannot get the disease again.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 16 April 2009
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Dianne OLeary,
% Models of Infection: Person to Person,
% Computing in Science and Engineering,
% Volume 6, Number 1, January/February 2004.
%
% Dianne OLeary,
% Scientific Computing with Case Studies,
% SIAM, 2008,
% ISBN13: 978-0-898716-66-5,
% LC: QA401.O44.
%
% Input:
%
% integer M, N, the number of rows and columns of beds.
%
% integer A(M,N), status of each patient on day T = 1.
%
% integer K, the maximum number of days of infection.
%
% real TAU, the probability of transmission of the disease
% over one day, due to one neighboring patient who is infected.
%
% integer T_MAX, the number of days to model.
%
% Output:
%
% real SIR(3,T_MAX), the relative numbers of susceptible,
% infected, and recovered patients. The sum of these three values
% will be 1 for each day.
%
sir = zeros(3,t_max);
for t = 1 : t_max
%
% Plot the current data.
%
timestep_display ( m, n, a, k, t );
%
% Compute SIR.
%
sir(1,t) = sum ( sum ( a == 0 ) );
sir(2,t) = sum ( sum ( 1 <= a & a <= k ) );
sir(3,t) = sum ( sum ( a == -1 ) );
%
% Update the patient status for the next day.
%
if ( t == t_max )
break
end
a_new = zeros ( m, n );
for i = 1 : m
for j = 1 : n
%
% Recovered patients never change.
%
if ( a(i,j) == -1 )
a_new(i,j) = -1;
%
% Infected, and less than K days, increase by 1.
%
elseif ( 1 <= a(i,j) && a(i,j) < k )
a_new(i,j) = a(i,j) + 1;
%
% Infected K days becomes recovered.
%
elseif ( a(i,j) == k )
a_new(i,j) = -1;
%
% Susceptible, look for infected neighbors.
%
else
a_new(i,j) = 0;
if ( 1 < i && 0 < a(i-1,j) && a(i-1,j) <= k )
if ( rand ( 1, 1 ) <= tau )
a_new(i,j) = 1;
end
end
if ( i < m && 0 < a(i+1,j) && a(i+1,j) <= k )
if ( rand ( 1, 1 ) <= tau )
a_new(i,j) = 1;
end
end
if ( 1 < j && 0 < a(i,j-1) && a(i,j-1) <= k )
if ( rand ( 1, 1 ) <= tau )
a_new(i,j) = 1;
end
end
if ( j < n && 0 < a(i,j+1) && a(i,j+1) <= k )
if ( rand ( 1, 1 ) <= tau )
a_new(i,j) = 1;
end
end
end
end
end
%
% Copy new data into A.
%
a = a_new;
end
%
% Normalize SIR.
%
sir(1:3,1:t_max) = sir(1:3,1:t_max) / m / n;
return
end