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Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate

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  • Teng, Zhidong
  • Wang, Lei

Abstract

In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is investigated. It is shown that the extinction and persistence of the disease in probability are determined by a threshold value R˜0. That is, if R˜0<1 and an additional condition holds then disease dies out, and if R˜0>1 then disease is weak permanent with probability one. To obtain the permanence in the mean of the disease, a new quantity R̂0 is introduced, and it is proved that if R̂0>1 the disease is permanent in the mean with probability one. Furthermore, the numerical simulations are presented to illustrate some open problems given in Remarks 1–3 and 5 of this paper.

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  • 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.
    • Handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:507-518
    DOI: 10.1016/j.physa.2016.01.084
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    Cited by:

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    7. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Wei, Xiang, 2017. "A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 198-208.
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    10. Zhang, Yan & Fan, Kuangang & Gao, Shujing & Liu, Yingfen & Chen, Shihua, 2019. "Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 671-685.

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