Analysis of an SIR model with saturating contact rate and carrier-dependent infectious diseases under the effect of environmental discharge (original) (raw)

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 contacts given by J. A. P. Heesterbeek and J. A. J. Metz [J. Math. Biol. 31, No. 5, 529–539 (1993; Zbl 0770.92021)]. 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 logistic growth of the carrier population. Stability analysis of this model is carried out using usual theory of nonlinear differential equations. 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 the intrinsic growth rate of the carrier population increase, the infective human population decreases and increases, respectively. It is concluded from the analysis that if the death rate of the carrier po...

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