Analysis of an SIR Model with Saturating Contact Rate and Carrier- Dependent Infectious Diseases under the Effect of Environmental Discharge*

Abstract

This paper deals with an SIR epidemic model that incorporates constant recruitment rate and disease caused death. We consider the saturating contact rate of individuals contact given by Heesterbeek and Metz1. The model for carrier-dependent infectious diseases, like cholera, diarrhea etc. caused by direct contact of susceptibles with infectives as well as by carriers is proposed and analyzed assuming the logistic growth of carrier population. Stability analysis of this model is carried out using usual theory of nonlinear
differential equation. The criteria for asymptotic and global stability of an interior equilibrium are obtained. By computer simulation it is shown that if the growth rate of recovery and intrinsic growth rate of carrier population increase, the infective human population decreases and increases respectively. It is concluded from the analysis that if the death rate of carrier population increases, both of the infective and carrier population decreases.