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.