一类具有病毒感染的随机传染病模型的平稳分布

郑亮; ZHENG Liang

doi:10.48014/fcpm.20230515001

一类具有病毒感染的随机传染病模型的平稳分布

Stationary Distribution of a Random Epidemic Model with Virus Infection

中国理论数学前沿 2023年第1卷第1期页码[21-30] 下载全文[0.6MB] [HTML]

摘要

自2020年年初以来, 世界一直面临着以COVID-19大流行形式出现的最大的病毒学入侵, 而新冠病毒的爆发再次说明传染病仍然是人类生存和发展的最大威胁之一。因此在本文中, 研究了一类考虑环境病毒影响的随机COVID-19传染病SEIW (W为环境中病毒的浓度) 模型的平稳分布的存在性。首先, 通过构建合适的Lyapunov函数证明了系统解的存在性与唯一性。然后使用随机Lyapunov方法建立了参数R^s₀, 并且证明了当R^s₀>1时, 系统解在R⁴₊上存在唯一的平稳分布。并且通过对比确定性模型的R₀和随机性模型的R^s₀, 可以发现R^s₀受到白噪声的影响, 并且R^s₀≤R₀, 当σ_i→0 (i=1, 2, 3, 4) 时, R^s₀→R₀, 说明本文的工作是对确定性模型的一个扩展, 并且当随机扰动较小时, 系统解在R⁴₊上存在唯一的平稳分布。

Abstract

Abstract: Since the beginning of 2020 the world has been facing the largest virological invasion in the form. of the COVID-19 pandemic, and the outbreak of COVID-19 has once again demonstrated that infectious diseases remain one of the greatest threats to human survival and development. In this paper, therefore, the existence of a stationary distribution for a class of stochastic COVID-19 infectious disease SEIW (W is the concentration of virus in the environment) models that take into account the effect of environmental viruses is investigated. First, the existence and uniqueness of the solution of the system are proved by constructing a suitable Lyapunov function. The parameters R^s₀ are then established using the stochastic Lyapunov method and the existence of a unique stationary distribution of the system solution on R⁴₊ when R^s₀ >1 is demonstrated. And by comparing the deterministic model of R₀ and the stochastic model of R^s₀ , it can be found that R^s₀ is influenced by white noise and R^s₀ ≤R₀, when σ_i →0 (i=1, 2, 3, 4) , R^s₀ →R₀, indicating that the work in this paper is an extension of the deterministic model and when the random perturbations are small, there exists a unique stationary distribution on R⁴₊ for the system solution.

DOI

10.48014/fcpm.20230515001

文章类型

研究性论文

收稿日期

2023-05-15

接收日期

2023-05-22

出版日期

2023-06-28

关键词

病毒感染, 随机传染病模型, 平稳分布

Keywords

Virus infection, stochastic infectious disease model, stationary distribution

作者

郑亮

Author

ZHENG Liang

所在单位

兰州理工大学理学院, 兰州 730050

Company

Lanzhou University of Technology, School of Science, Lanzhou 730050, China

浏览量

773

下载量

472

基金项目

甘肃省自然科学基金(资助号21JR7RA216)

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引用本文

郑亮. 一类具有病毒感染的随机传染病模型的平稳分布[J]. 中国理论数学前沿, 2023, 1(1): 21-30.

Citation

ZHENG Liang. Stationary distribution of a random epidemic model with virus infection[J]. Frontiers of Chinese Pure Mathematics, 2023, 1(1): 21-30.