Deterministic and Stochastic models of SIR Epidemic – A Review

Abstract

This paper presents a review of mathematical models developed for Epidemics over the past 25 years. The evolution of models of SIR(Susceptible-Infectious-Removed) epidemics which is the classic epidemic model developed for infectious diseases is discussed. Though there are 5000+ articles available in the research arena,it has been taken some of the articles in the past 25 years for the evolution of the refinement of the models over time. Theseselected articles describe the Epidemic models with different situations, problem areas, challenges with different techniques,modellingwith various problem structures and techniques such as discrete time/continuous time state space, transform techniques, Kinetic theory etc. and different distributions of the stochastic variables used. The models have been derived with different techniques,simulation techniques are the common numerical technique in many of the articles for the case studies of interest.