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Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

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  • Qixing Han
  • Daqing Jiang
  • Chengjun Yuan

Abstract

We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individuals to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.

Suggested Citation

  • Qixing Han & Daqing Jiang & Chengjun Yuan, 2013. "Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    • Handle: RePEc:hin:jnlaaa:127321
    DOI: 10.1155/2013/127321
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    Cited by:

    1. Wei, Fengying & Chen, Lihong, 2020. "Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Hussain, Shah & Tunç, Osman & Rahman, Ghaus ur & Khan, Hasib & Nadia, Elissa, 2023. "Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 130-150.
    3. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    4. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    5. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.

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