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Nontrivial periodic solution of a stochastic seasonal rabies epidemic model

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  • Cao, Zhongwei
  • Feng, Wei
  • Wen, Xiangdan
  • Zu, Li
  • Gao, Jinyao

Abstract

In this paper, we consider a stochastic nonautonomous rabies epidemic model. By using Khasminskii’s theory of periodic solutions and constructing a suitable stochastic Lyapunov function, we show that the stochastic nonautonomous epidemic model admits at least one nontrivial positive T-periodic solution under certain condition.

Suggested Citation

  • Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li & Gao, Jinyao, 2020. "Nontrivial periodic solution of a stochastic seasonal rabies epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119318801
    DOI: 10.1016/j.physa.2019.123361
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 837-845.
    4. 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:

    1. 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).
    2. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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