So, I used Mathematica to create a basic SIR Disease model using the following equations:
Neqs=eqs/.{b->u,a->0}
eqs={
S'[t] == b N[t] - u S[t] - B S[t](I[t] / N[t]),
I'[t] == B S[t] (I[t] / N[t]) - u I[t] - a I[t] - g I[t],
R'[t] == g I[t] - u R[t],
N'[t] == b N[t] - u N[t] - a I[t],
S[0] == N[0] - I[0],
I[0] == 1,
R[0] == 0,
N[0] == n
}
I then used Manipulate
to find the solution using NDSolve
and then plot it.
This code all worked and I have some neat sliders for $u$, $B$, $g$, and $n$ that are pretty fun to play around with.
Now, I am supposed to solve for the equilibrium, or when the disease spreads ($dI/dt > 0$), and plot the isoclines for $S$ and $I$ populations. I tried to write an if loop to do this, but I am really confused and it just gives me errors. Does anyone know a way to approach this? Any help is appreciated!
Best Answer
Is that "BSt" supposed to be B*S[t] or is it B*S[t]*t? If the latter, this is a time-dependent system, not an autonomous system, and there is no such thing as an equilibrium. All the SIR models I've seen would have a term involving S[t]*I[t], to model susceptibles becoming infective by contact with infectives.