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Dynamics of a stochastic avian–human influenza epidemic model with mutation

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  • Zhang, Xinhong
  • Shi, Zhenfeng
  • Wang, Yuanyuan

Abstract

In this paper, an avian–human influenza epidemic model perturbed by environmental white noise is investigated. This model allows the transmission of avian influenza and its mutant. Our stochastic avian influenza model has no equilibria because of perturbation of environmental noise, but similar dynamics as those in the deterministic model can be obtained. For the bird sub-system, critical value between extinction and persistence of the infected bird population is obtained. For the full stochastic avian–human system, different thresholds are obtained, persistence and global qualitative behaviors are discussed. It is shown, using Has’minskii theory and stochastic Lyapunov function, that an ergodic stationary distribution exists. Finally, numerical simulations are given to support the theoretical results.

Suggested Citation

  • Zhang, Xinhong & Shi, Zhenfeng & Wang, Yuanyuan, 2019. "Dynamics of a stochastic avian–human influenza epidemic model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119305096
    DOI: 10.1016/j.physa.2019.121940
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    References listed on IDEAS

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    Cited by:

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    8. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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