Chapter 7.P1, Problem 7P

Use the equation $S+I+R=N$ to reduce the SIRS model (3) to a system of dimension $2$.

Then use the qualitative methods of Chapter 7 and numerical simulations to discover as much as you can about the properties of the system (3). Compare and contrast your finding with the properties of solutions of the SIR model.

$\begin{array}{c}S\text{'}=-\beta IS+\gamma R,\\ I\text{'}=\beta IS-v\mathrm{I},\\ R\text{'}=vI-\gamma R.\end{array}$ (3)