Electron. J. Diff. Equ., Vol. 2015 (2015), No. 304, pp. 1-8.

Global stability of SIR models with nonlinear incidence and discontinuous treatment

Mei Yang, Fuqin Sun

Abstract:
In this article, we study an SIR model with nonlinear incidence rate. By defining the Filippov solution for the model and constructing suitable Lyapunov functions, we show that the global dynamics are fully determined by the basic reproduction number $R_0$, under certain conditions on the incidence rate and treatment functions. When $R_0\leq 1$ the disease-free equilibrium is globally asymptotically stable, and when $R_0>1$ the unique endemic equilibrium is globally asymptotically stable.

Submitted November 3, 2014. Published December 16, 2015.
Math Subject Classifications: 34A36, 34A60, 34D23.
Key Words: Filippov solution; discontinuous treatment; reproduction number; asymptotic stability.

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Mei Yang
College of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: yangmei19890610@yeah.net
Fuqin Sun
College of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: sfqwell@163.com

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