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Abstract
In this paper, weconstruct and analyze a model for the linking of within- andbetween-host with saturation incidence rate. It is postulated thatthe infection process depends on the size of the infective inoculumthat susceptible hosts may acquire by interacting with acontaminated environment. Since the dynamical processes associatedwith the within- and between-host occur on different time scales,the dynamical behaviors of the system can be analyzed by using asingular perturbation argument, which allows us to decouple the fullsystem by separating the fast- and slow-systems. For the fastsystem, it is shown that the infection-free equilibrium U_0 islocally asymptotically stable if R_{v^0}<1, whereas U_0 isunstable if R_{v^0}>1, and a unique interior equilibrium U^*(E) exists and it is locally asymptotically stable. For theslow system, under the condition that the fast system has a stableinterior equilibrium U^*(E) ( i.e., R_{v^0}>1), there existsat least one endemic equilibrium W^* if R_h>1. We also getthe sufficient condition for its local stability of the endemicequilibrium W^*. At last, some simple discussion is presented atthe end of the article.
How to Cite this Article:
Mimi Yan, Ruiqing Shi, Zhuchao Ji, Analysis of an SIR epidemic model with saturation incidence rate in an environmentally-driven infectious disease, Journal of Nonlinear Functional Analysis 2015 (2015), Article ID 10.