Analysis of Numerical and Exact solutions of certain SIR and SIS Epidemic models

摘要

We study here a particular case of SIR and SIS epidemic models for a given constant population. These mathematical models are described by coupled nonlinear first order differential equations. Exact solutions are computed by linearizing the term in the resulting differential equation for the infective population. We then compare the exact solution with the numerical, using a Runge-Kutta algorithm implemented by MathCAD software. The profiles of the solutions are provided from which we infer that the numerical and exact solutions agreed very well. However for the SIR model the approximation in the derivation of the exact solution made this to deviate slightly from the numerical, for small initial population of susceptibles. For larger values it is observed that this deviation becomes negligible.