Author(s)

Fumin Zhang, Shujing Gao, Yujiang Liu, Yan Zhang

Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, China.

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.

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

Zhang, F. , Gao, S. , Liu, Y. and Zhang, Y. (2016) Dynamics of a Nonautonomous SIR Model with Time-Varying Impulsive Release and General Nonlinear Incidence Rate in a Polluted Environment. Applied Mathematics, 7, 681-693. doi: 10.4236/am.2016.77062.