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A stochastic SEIRS rabies model with population dispersal: Stationary distribution and probability density function

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

Abstract

In this paper, we propose a stochastic SEIRS rabies epidemic models with two patches to investigate the spatial spread of rabies under the influence of environmental noise. Adopting a new technique to construct the stochastic Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution. In addition, if the movement of dogs is forbidden, we obtain the exact expression of probability density function around a quasi-equilibrium point. Finally, numerical simulations are employed to verify our analytical results and reveal the impact of stochastic perturbations on rabies transmission.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002636
    DOI: 10.1016/j.amc.2022.127189
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. 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).
    5. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    6. 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).
    7. S. P. Rajasekar & M. Pitchaimani & Quanxin Zhu & Kaibo Shi, 2021. "Exploring the Stochastic Host-Pathogen Tuberculosis Model with Adaptive Immune Response," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-23, June.
    8. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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