What do you mean precisely with that? Physically, the model conserves S+I=1, so yes, actually evolving the model with initial conditions that satisfy S+I = 1 would keep it on this manifold. But that’s not what
streamplotdoes. it just plots the vector field.
I think the trajectories supposed to strictly on the line of S+I=1, and the phase portrait of SIS model is like this:
You can’t use
streamplotfor what you want.
I initially found the solution in the post Plotting a phase portrait of a differential equation is streamplot, so I use it. am I misunderstanding?
Also, I am not sure whether the following understanding is correct:
Plotting the vector field: plot the vector on each point, its direction is obtained according to the differential equations (\frac{dS}{dt},\frac{dI}{dt},\frac{dR}{dt}). So, we can use streamplot.
Plotting the phase space
plot trajectories starting from every possible initial
state (initial condition). And, your suggestion is quiver plot?
Thanks!