The dynamics of a stochastic SEI model with standard incidence and infectivity in incubation period

Ping Zhu; Yongchang Wei; Ping Zhu; Yongchang Wei

doi:10.3934/math.20221002

AIMS Mathematics

2022, Volume 7, Issue 10: 18218-18238. doi: 10.3934/math.20221002

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The dynamics of a stochastic SEI model with standard incidence and infectivity in incubation period

Ping Zhu ¹,
Yongchang Wei ^{2
,
,}

1.
Department of Mathematics, Luoyang Normal University, Luoyang, 471934, China
2.
School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

Received: 19 June 2022 Revised: 31 July 2022 Accepted: 08 August 2022 Published: 11 August 2022
MSC : 34D05, 60H10

This paper focuses on the long time dynamics for a class stochastic SEI model with standard incidence and infectivity in incubation period. Firstly, we investigate a unique global positive solution almost surely for any positive initial value. Secondly, we obtain a unique stationary measure and the extinction condition of the epidemic based on the technique of Lyapunov function and inequalities. Thirdly, we explore the asymptotic behavior of the solutions around equilibriums of the corresponding deterministic model from different aspects. Finally, we establish some numerical simulations to illustrate the main presented results.
- SEI model,
- existence and uniqueness,
- stationary measure,
- extinction,
- asymptotic behavior
Citation: Ping Zhu, Yongchang Wei. The dynamics of a stochastic SEI model with standard incidence and infectivity in incubation period[J]. AIMS Mathematics, 2022, 7(10): 18218-18238. doi: 10.3934/math.20221002

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Abstract

This paper focuses on the long time dynamics for a class stochastic SEI model with standard incidence and infectivity in incubation period. Firstly, we investigate a unique global positive solution almost surely for any positive initial value. Secondly, we obtain a unique stationary measure and the extinction condition of the epidemic based on the technique of Lyapunov function and inequalities. Thirdly, we explore the asymptotic behavior of the solutions around equilibriums of the corresponding deterministic model from different aspects. Finally, we establish some numerical simulations to illustrate the main presented results.

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