The Unique ergodic stationary distribution of two stochastic SEIVS epidemic models with higher order perturbation

Yan Xie; Zhijun Liu; Yan Xie; Zhijun Liu

doi:10.3934/mbe.2023060

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 1317-1343. doi: 10.3934/mbe.2023060

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The Unique ergodic stationary distribution of two stochastic SEIVS epidemic models with higher order perturbation

Yan Xie ,
Zhijun Liu ^,

School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China

Academic Editor: Sanling Yuan

Received: 17 August 2022 Revised: 30 September 2022 Accepted: 16 October 2022 Published: 27 October 2022

Two types of susceptible, exposed, infectious, vaccinated/recovered, susceptible (SEIVS) epidemic models with saturation incidence and temporary immunity, driven by higher order white noise and telegraph noise, are investigated. The key aim of this work is to explore and obtain the existence of the unique ergodic stationary distribution for the above two models, which reveals whether the disease will be prevalent and persistent under some noise intensity assumptions. We also use meticulous numerical examples to validate the feasibility of the analytical findings. Finally, a brief biological discussion shows that the intensities of noises play a significant role in the stationary distributions of the two models.
- SEIVS epidemic model,
- higher order white noise,
- telegraph noise,
- stationary distribution,
- ergodicity
Citation: Yan Xie, Zhijun Liu. The Unique ergodic stationary distribution of two stochastic SEIVS epidemic models with higher order perturbation[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 1317-1343. doi: 10.3934/mbe.2023060

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Abstract

Two types of susceptible, exposed, infectious, vaccinated/recovered, susceptible (SEIVS) epidemic models with saturation incidence and temporary immunity, driven by higher order white noise and telegraph noise, are investigated. The key aim of this work is to explore and obtain the existence of the unique ergodic stationary distribution for the above two models, which reveals whether the disease will be prevalent and persistent under some noise intensity assumptions. We also use meticulous numerical examples to validate the feasibility of the analytical findings. Finally, a brief biological discussion shows that the intensities of noises play a significant role in the stationary distributions of the two models.

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