Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840875 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 8 Pages |
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.
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Zhenguo Bai, Yicang Zhou, Tailei Zhang,