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Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence

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  • Lahrouz, Aadil
  • Omari, Lahcen

Abstract

The present paper studies a stochastic SIRS epidemic model with general incidence rate in a population of varying size. Sufficient conditions for the extinction and the existence of a unique stationary distribution are obtained. The analytical results are illustrated by computer simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:960-968
    DOI: 10.1016/j.spl.2012.12.021
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    1. Beretta, Edoardo & Kolmanovskii, Vladimir & Shaikhet, Leonid, 1998. "Stability of epidemic model with time delays influenced by stochastic perturbations1This paper was written during a visit of V. Kolmanovskii and L. Shaikhet in Italy (Napoli, Urbino).1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(3), pages 269-277.
    2. Lahrouz, A. & Omari, L. & Kiouach, D. & Belmaâti, A., 2011. "Deterministic and stochastic stability of a mathematical model of smoking," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1276-1284, August.
    3. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    4. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    5. 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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