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
,
under certain conditions on the
incidence rate and treatment functions. When
the disease-free
equilibrium is globally asymptotically stable, and when
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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