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Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence

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Listed:
  • Liu, Qun
  • Jiang, Daqing
  • Shi, Ningzhong
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we consider a stochastic SIRS epidemic model with standard incidence. By constructing suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of ergodic stationary distribution of the model. Moreover, we also establish sufficient conditions for extinction of the disease.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    • Handle: RePEc:eee:phsmap:v:469:y:2017:i:c:p:510-517
    DOI: 10.1016/j.physa.2016.11.077
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    References listed on IDEAS

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    1. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    2. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    3. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    4. 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.
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