How to solve a vector field ODE?

Questions
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1

Hi, I am trying to set up a code to plot a streamplot from the results from a SIR model.

The problem to solve is
r′=F(r)

where r=(x,y) and F(x,y)=(−bxy/n,bxy/n−k*y)

and where
b=3.3925;
k=2.95;
n=157759;

How can I set up this StreamPlot of the solutions for this SIR problem?

Thanks

2

I’m not sure I fully understand, but would this be along the lines of what you’re looking for, except for the simplified parameter values and some arbitrary choice of range?

StreamPlot[{-b x y/n, b x y/n - k y} /. {b → 3.4, k → 3,
n → 160}, {x, -100, 100}, {y, -100, 100}]