Page - 236 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

236 8 SolvingOrdinaryDifferentialEquations Fig. 8.13 Including loss of immunity Fig. 8.14 Increasingβ and reducingν compared to Fig.8.13 8.3.8 IncorporatingVaccination We can extend the model to also include vaccination. To this end, it can be useful to track those who are vaccinatedand those who are not. So, we introducea fourth category, V, for those who have taken a successful vaccination. Furthermore, we assume that in a time intervalΔt, a fractionpΔt of the S category is subject to a successfulvaccination.Thismeansthat in the timeΔt,pΔtS people leavefromthe S to the V category. Since the vaccinated ones cannot get the disease, there is no impacton the I or Rcategories.We canvisualize the categories, and the movement between them,as