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Dynamics of an avian influenza model with half-saturated incidence

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  • Shi, Zhenfeng
  • Zhang, Xinhong
  • Jiang, Daqing

Abstract

In this paper, an avian influenza epidemic model with half saturated incidence is investigated. Firstly we study the local asymptotical stability of equilibria of the deterministic model. Then for the stochastic model, the existence of the global positive solution is proved and different thresholds are obtained. In addition, we get sufficient conditions for the existence of an ergodic stationary distribution by using Has’minskii theory and Lyapunov function. Finally, some numerical simulations illustrate the analytical results.

Suggested Citation

  • Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:399-416
    DOI: 10.1016/j.amc.2019.02.070
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    References listed on IDEAS

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    2. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
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    5. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
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    Cited by:

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    2. Zhou, Baoquan & Zhang, Xinhong & Jiang, Daqing, 2020. "Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Fehaid Salem Alshammari & Fahir Talay Akyildiz, 2023. "Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process," Mathematics, MDPI, vol. 11(18), pages 1-15, September.
    5. 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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    7. Wang, Haile & Zuo, Wenjie & Jiang, Daqing, 2023. "Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    8. Shi, Zhenfeng & Jiang, Daqing & Zhang, Xinhong & Alsaedi, Ahmed, 2022. "A stochastic SEIRS rabies model with population dispersal: Stationary distribution and probability density function," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    9. 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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