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http://dx.doi.org/10.1016/j.cnsns.2008.01.009

has been cited by the following article:

• TITLE: Dynamics of a Nonautonomous SIR Model with Time-Varying Impulsive Release and General Nonlinear Incidence Rate in a Polluted Environment

  AUTHORS: Fumin Zhang, Shujing Gao, Yujiang Liu, Yan Zhang

  KEYWORDS: Nonautonomous SIR Model, Varying Pulses, General Nonlinear Incidence Rate, Global Attractivity

  JOURNAL NAME: Applied Mathematics, Vol.7 No.7, April 28, 2016

  ABSTRACT: In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.