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The threshold of a stochastic delayed SIR epidemic model with temporary immunity

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  • Liu, Qun
  • Chen, Qingmei
  • Jiang, Daqing

Abstract

This paper is concerned with the asymptotic properties of a stochastic delayed SIR epidemic model with temporary immunity. Sufficient conditions for extinction and persistence in the mean of the epidemic are established. The threshold between persistence in the mean and extinction of the epidemic is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

Suggested Citation

  • Liu, Qun & Chen, Qingmei & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 115-125.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:115-125
    DOI: 10.1016/j.physa.2015.12.056
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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. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
    3. Carletti, M. & Burrage, K. & Burrage, P.M., 2004. "Numerical simulation of stochastic ordinary differential equations in biomathematical modelling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 271-277.
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