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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. 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).
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    4. 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).
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    6. 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.
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