Article ID Journal Published Year Pages File Type
840875 Nonlinear Analysis: Theory, Methods & Applications 2011 8 Pages PDF
Abstract

We study an SIR model with a seasonal contact rate and a staged treatment strategy, which is an extension of our previous work [Z. Bai, Y. Zhou, Existence of two periodic solutions for a non-autonomous SIR epidemic model, Appl. Math. Model. 35 (2011) 382–391]. It is proved that the persistence and extinction of the disease are determined by the basic reproductive number (R0R0) and a threshold parameter (RcRc). It is obtained that the model exhibits two different bistable behaviors under certain conditions: the stable disease-free state coexists with a stable endemic periodic solution, and three endemic periodic solutions coexist with two of them being stable. Numerical simulations are presented to illustrate theoretical results.

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