A note on Exact solution of SIR and SIS epidemic models

TL;DR

This paper presents an exact, parameter-free solution to specific SIR and SIS epidemic models, challenging the common belief that such models cannot be solved exactly, thus providing a valuable addition to epidemiological modeling.

Contribution

It provides the first exact solution for a particular case of SIR and SIS models without any parameter restrictions, advancing analytical methods in epidemiology.

Findings

Derived an exact solution for the models

No limiting conditions on parameters

Enhances understanding of epidemic dynamics

Abstract

In this article we have successfully obtained an exact solution of a particular case of SIR and SIS epidemic models given by Kermack and Mckendrick [1] for constant population, which are described by coupled nonlinear differential equations. Our result has no limiting conditions for any parameter involved in the given models. In epidemiology many researchers believe that it is very hard to get an exact solution for such models. We hope this solution will be an opening window and good addition in the area of epidemiology.