| Volume 10, Number 4, 2020, Pages 1396-1415 DOI：10.11948/20190214 |
| Dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate |
| Wenjie Cao,Tao Pan |
| Keywords:SIR epidemic model, stochastic perturbation, impulsive effect, periodic solution, global attraction. |
| Abstract: |
| In this paper, the dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate are analyzed. The existence and uniqueness of the global positive solution is proved by constructing the equivalent system without pulses. The threshold which determines the extinction and persistence of the disease is obtained. The global attraction of disease-free periodic solution is addressed. Sufficient condition for the existence of a positive periodic solution is established. These results are supported by computer simulations. |
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