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