Milstein method for Stochastic SIR model - Mathlab program - Graph shows that deterministic not stochastic

Question

0 个投票

clf
A=12;
la=0.01;
d=0.1;
ep=0.01;
mu=0.1;
r=2;
al=1;
k=0.1;
si= 0.01;
randn('state',1)
T = 300; Delta = 2^(-10); delta = Delta^2;     
L = T/Delta; K = Delta/delta;
S = zeros(1,L+1); 
I = zeros(1,L+1); 
R = zeros(1,L+1);
S(1) = 60;
I(1) = 20;
R(1) = 20;
for n = 1:L
     Winc1 = 0;
    for k = 1:K
       Winc1 = sqrt(delta)*randn;
    end
    S(n+1) = S(n) + (A-d*S(n)-((la*S(n)*I(n))/(1+k*I(n))))*Delta- ...
                 ((si*S(n)*I(n))/(1+k*I(n)))*Winc1*sqrt(Delta)+...
                 0.5*si^2*((S(n)*I(n))/(1+k*I(n)))*Delta*(Winc1^2 - 1);
    I(n+1) = I(n)+ Delta*(((la*S(n)*I(n))/(1+k*I(n)))-(d+ep+mu)*I(n)-
(r*I(n))/(1+al*I(n)))+...
                ((si*S(n)*I(n))/(1+k*I(n)))*Winc1*sqrt(Delta)+...
                 0.5*si^2*((S(n)*I(n))/(1+k*I(n)))*Delta*(Winc1^2 - 1);
    R(n+1) = R(n) + (mu*I(n)+(r*I(n)/(1+I(n)*al))-d*R(n))*Delta;
end
subplot(231)
plot([0:Delta:T],S,'r-'), hold on
subplot(232)
plot([0:Delta:T],I,'g-')
subplot(233)
plot([0:Delta:T],R,'b-')

What can i do to get graph interms of stochastic increments. The given mathlab program graph does not include stochastic increments. May i know what term is missing in the above program. In out Stochastic SIR model:

S'(t) = (A-d*S(t)-((la*S(t)*I(t))/(1+k*I(t))))* dt -
        ((si*S(t)*I(t))/(1+k*I(t)))*dW(t);
I'(t) = (((la*S(t)*I(t))/(1+k*I(t)))-(d+ep+mu)*I(t)- (r*I(t))/(1+al*I(t)))*dt+...
         ((si*S(t)*I(t))/(1+k*I(t)))*dW(t);
R'(t) = (mu*I(t)+(r*I(t)/(1+I(t)*al))-d*R(t))*dt;
kindly help me.

I thank you.