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| Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth |
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| KeyWord:Logistic growth Saturated treatment Stationary distribution and ergodicity Non-monotone incidence Extinction |
| Author Name | Affiliation | | Yubo Liu | College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China | | Jianli Li | College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China | | Daipeng Kuang | College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, China |
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| Abstract: |
| In this paper, a stochastic SIR epidemic model with saturated treatment function, non-monotone incidence rate and logistic growth is studied. First, we prove that the stochastic model has a unique global positive solution. Next, by constructing a suitable Lyapunov function, we can show that there exists an ergodic stationary distribution in the random SIR model. Then, we show that a sufficient condition can make the disease tend to extinction. Finally, some numerical simulations are used to prove our analytical result. |
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