Existence of multiple periodic solutions for an SIR model with seasonality |
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Authors: | Zhenguo Bai Yicang ZhouTailei Zhang |
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Institution: | Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China |
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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 (R0) and a threshold parameter (Rc). 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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Keywords: | 34K13 92D30 37N25 |
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