2024年4月21日 星期日
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
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Rs0, 并且证明了当Rs0>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Rs0, 可以发现Rs0受到白噪声的影响, 并且Rs0≤R0, 当σi→0 (i=1, 2, 3, 4) 时, Rs0→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 Rs0 are then established using the stochastic Lyapunov method and the existence of a unique stationary distribution of the system solution on R4+ when Rs0 >1 is demonstrated. And by comparing the deterministic model of R0 and the stochastic model of Rs0 , it can be found that Rs0 is influenced by white noise and Rs0 ≤R0, when σi →0 (i=1, 2, 3, 4) , Rs0 →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.  

DOI10.48014/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
KeywordsVirus infection, stochastic infectious disease model, stationary distribution
作者郑亮
AuthorZHENG Liang
所在单位兰州理工大学理学院, 兰州 730050
CompanyLanzhou University of Technology, School of Science, Lanzhou 730050, China
浏览量283
下载量197
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.
CitationZHENG Liang. Stationary distribution of a random epidemic model with virus infection[J]. Frontiers of Chinese Pure Mathematics, 2023, 1(1): 21-30.