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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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    1. Zhao, Yu & Zhang, Liping & Yuan, Sanling, 2018. "The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 248-260.
    2. Yanli Zhou & Weiguo Zhang & Sanling Yuan, 2013. "Survival and Stationary Distribution in a Stochastic SIS Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    3. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    4. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    5. 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.
    6. 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.
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    Cited by:

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    8. Su, Tan & Yang, Qing & Zhang, Xinhong & Jiang, Daqing, 2023. "Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).

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