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Stability of SIRS system with random perturbations

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  • Lu, Qiuying

Abstract

Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is an SIRS model with or without distributed time delay influenced by random perturbations. We present the stability conditions of the disease-free equilibrium of the associated stochastic SIRS system.

Suggested Citation

  • Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:18:p:3677-3686
    DOI: 10.1016/j.physa.2009.05.036
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    References listed on IDEAS

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    1. 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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    Cited by:

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    16. 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.
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