Matlab:Refined population model

```%
% REFINED MAGICAL GIRL-WITCH POPULATION MODEL
% BASIC MAGICAL GIRL-WITCHES MODEL
% This file has been produced for Matlab 7.4.0
% It is 100% compatible with FreeMat 4.0, however, you may want to change the plot commands to
% plot(M, 'g.-') and plot(W, 'r.-') for aesthetics purpose
%
%
% If you want to modify the constants, please bear these restrictions in mind:
% -C should be an integer
% -D, B, F, K should be values in [0,1]
% -B should be greater than K (or else, the number of witches will be negative)
% -W(1) should be strictly positive. If W(1)=0, no witch appear ever, and MSes grow linearily
%

C = 100;     % Number of girls contracted by QBe
D = 0.200;    % Proportion of girls (who are fighting) that die
B = 0.100;   % Proportion of girls (who are fighting) to become witches
F = 0.015;   % Proportion of familiars becoming witches
K = 0.096;    % Proportion of witches getting killed by MSes

steps = 500; % Number of iterations for the simulation

M(1) = 0;    % Number of magical girls at first
W(1) = 1;    % Number of witches at first

hold on

for t=1:steps
prop = min(M(t), W(t));

deltaM = C- prop*(D+B);
deltaW = F*W(t) + prop*(B-K);

M(t+1)=M(t)+deltaM;
W(t+1)=W(t)+deltaW;
end

title('Evolution of the Magical Girls population over time')
xlabel('time')
ylabel('number of magical girls/witches')
plot(M, 'g-')
plot(W, 'r-')
legend('Magical Girls', 'Witches', 'location', 'northeast')
legend('boxoff')

hold off

```