Question

dS/dt = vR - ?SI

dI/dt = ?SI – ?I

dR/dt = ?I - vR.

Consider a SIRS model.

Modify the above equations to include vital dynamics (births and deaths from causes other than infection) such that all progeny of infected individuals are born infected. Be sure to clearly define any new variables or parameters. Explain the changes you have made.

Answer 1

We can also add vital dynamics to a SIRS model, where and again represent the birth and death rates, respectively. To maintain a constant population, assume that  . In steady state  
dl dt 0
. The ODE then becomes:

where is the total population.