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Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients

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  • Rifhat, Ramziya
  • Wang, Lei
  • Teng, Zhidong

Abstract

In this paper, we investigate the dynamics of a class of periodic stochastic SIS epidemic models with general nonlinear incidence f(S,I). Some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established. By using the Khasminskii’s boundary periodic Markov processes, the existence of stochastic nontrivial periodic solution for the models is also obtained. The numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented.

Suggested Citation

  • Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:176-190
    DOI: 10.1016/j.physa.2017.04.016
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
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    6. 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.
    7. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
    8. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
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    Cited by:

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    4. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    5. Gao, Shujing & Zhong, Deming & Zhang, Yan, 2018. "Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 162-171.

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