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Critical result on the threshold of a stochastic SIS model with saturated incidence rate

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  • Zhu, Chunjuan

Abstract

In this paper, we discuss the threshold R0̃ of a stochastic SIS epidemic model with saturated incidence based on [10]. If R0̃<1, the disease will die out for any intensity noise σ2>0, which is not proved in [10]. Then, it is obtained that the disease will also go to extinction in probability if R0̃=1, which has been left as an open problem in [10] and many other literatures. And when R0̃>1, we get the stochastic persistence of the disease (which is different from the persistence in mean in previous literatures) by using Chebyshev’s inequality. And it shows the smaller noise will strengthen the stability of systems. Besides, the existence of the stationary distribution is gotten. Finally, numerical simulations are given to illustrate the results.

Suggested Citation

  • Zhu, Chunjuan, 2019. "Critical result on the threshold of a stochastic SIS model with saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 426-437.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:426-437
    DOI: 10.1016/j.physa.2019.02.012
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    1. Teng, Zhidong & Wang, Lei, 2016. "Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 507-518.
    2. Shufan Wang & Zhihui Ma, 2012. "Analysis of an Ecoepidemiological Model with Prey Refuges," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-16, November.
    3. Liu, Meng & Yu, Jingyi & Mandal, Partha Sarathi, 2018. "Dynamics of a stochastic delay competitive model with harvesting and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 335-349.
    4. Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
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