I'm mathematically modeling yellow fever, and yet, after assembling the model, I need to find the stationary states of the model. I had to do it by hand because wolfram software could not get the necessary values.
My question is, how do I check if my stationary states are in line with my biological model?
I was told that there is a way to verify this by performing a substitution of the s values of the points within my own template code. But I have no idea how to do it.
The code used is taking forever to get back to me as this data behaves in my model
function ypsir = ypsirtry(t,y)
betah = .01;
muh = 0.01;
sigmah = 0.05;
alphah = 0.06;
deltah = 0.05;
mui = 0.07;
mum = 0.07;
betai = 0.03;
lambdai = 0.06;
lambdah = 0.5;
k = 500;
ypsir = zeros(5,1);
ypsir(1) = sigmah*y(3) - muh*y(1) - betah*y(1)*y(5) + lambdah*(y(2)+ y(3) +
y(1));
ypsir(2) = -deltah*y(2) - y(2)*(alphah + muh) + betah*y(5)*y(1);
ypsir(3) = deltah*y(2) - sigmah*y(3);
ypsir(4) = -mui*y(4) - mum*y(4) - betai*y(2)*y(4) + lambdai*(y(4) + y(5))*(1
- (y(4) + y(5))/k);
ypsir(5) = betai*y(2)*y(4) - mui*y(5) - mum*y(5);
end
Along with this calling program
clear;
to = 0;
tf =50;
yo = [99 1 0 1 3];
[t y] = ode45(@(t,y)ypsirtry(t,y),[to tf],yo);
plot(t,y(:,1),t,y(:,2),t,y(:,3),t,y(:,4),t,y(:,5))
title('First Model of Yellow Fever')
xlabel('time')
ylabel('susceptible, infected, recovered,Mosquito Non-carrier, Carrier
mosquito')
My stationary states are:
S = (1/betai)*[(muh+alphah)+(sigmah/deltah)*deltah]*(mui+mum)/betai*N*I);
I = sigmah*R/deltah;
R = ((muh/betah + lambdah)*(muh+alphah))/(sigmah+lamdah)-(muh+alphah)*
(deltah/sigmah*deltah)-(betah/muh - lambdah)*(betai*N*I)*
(delta/sigmah*deltah));
N = -k/lambdai((-lamdai+(lambdai/k))*P/-betai*I + lambdai - (2k/lambdai*P)-
mui-mum);
P = betai*N*I/(mui+mum);
At where S = susceptible I = infected R = retweeted N = non-carrier mosquito P = carrier mosquito
betah
and so on) then that would also be a good test. $\endgroup$