function[P]=logistic(params,t)
% This m-file evaluates the logistic function, which is the solution of the
% differential equation
%
%  dP/dt = beta*P(M-P), P(0)=P_0. 
%
% Variables:
%
% t   = time
% P_0 = initial number of cases
% M   = carrying capacity for disease
% beta = growth rates for small P

global ParamsWeightLogistic
W    = ParamsWeightLogistic;

M    = W(1)*params(1);
beta = W(2)*params(2);
P_0  = 494;

P = P_0*M ./ ( P_0 + (M-P_0)*exp(-M*beta*t) );