function timestep_display ( m, n, a, k, t )
%*****************************************************************************80
%
%% timestep_display() displays the SIR status of all patients at one timestep.
%
% 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.
%
% The dynamics for how the disease starts and spreads are handled elsewhere.
% This routine simply displays the patient status on a given day.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 16 April 2009
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Dianne O'Leary,
% 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), the status of each patient:
% 0, "Susceptible", display as WHITE.
% 1 through K, "Infected", display as shades of RED.
% -1, "Recovered", display as GRAY.
%
% integer K, the maximum number of days of infection.
%
% integer T, the index of the current day.
%
%
% Clear the graphics frame.
%
clf ( );
%
% Determine the plot range.
%
margin = 0.05;
x_axes_min = 1.0 - 0.5 - margin;
x_axes_max = m + 0.5 + margin;
y_axes_min = 1.0 - 0.5 - margin;
y_axes_max = n + 0.5 + margin;
%
% Fill in the background with black.
%
x1 = x_axes_min;
x2 = x_axes_max;
y1 = y_axes_min;
y2 = y_axes_max;
rgb = [ 0.0, 0.0, 0.0 ];
fill ( [ x1, x2, x2, x1 ], [ y1, y1, y2, y2 ], rgb );
hold ( 'on' );
%
% Draw a square, representing the bed,
% with most of the length and width, centered at (I,J).
%
% Recovered patients have a light gray bed.
% Suspectible patients have a green bed.
% Infected patients are very red on the first day, then fade to gray.
%
for i = 1 : m
for j = 1 : n
x1 = i - 0.47;
x2 = i + 0.47;
y1 = j - 0.47;
y2 = j + 0.47;
if ( a(i,j) == -1 )
rgb = [ 0.8, 0.8, 0.8 ];
elseif ( a(i,j) == 0 )
rgb = [ 0.0, 0.8, 0.0 ];
else
rgb = ( ( k + 1 - a(i,j) ) * [1.0, 0.0, 0.0] ...
+ ( a(i,j) ) * [0.8, 0.8, 0.8] ) ...
/ ( k + 1 );
end
fill ( [ x1, x2, x2, x1 ], [ y1, y1, y2, y2 ], rgb );
hold on
end
end
%
% Make a title.
%
title_string = sprintf ( 'Patient status at day T = %d', t );
title ( title_string, 'fontsize', 16 );
%
% Choose the aspect ratio and other plot details.
%
axis ( [ x_axes_min, x_axes_max, y_axes_min, y_axes_max] );
axis equal
axis tight
hold ( 'off' );
pause ( 3 );
return
end