具有病毒感染的随机流行病模型的平稳分布

Zheng Liang
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引用次数: 0

摘要

摘要:自2020年初以来,世界一直面临着最大的病毒学入侵形式。新冠肺炎疫情再次证明,传染病仍然是人类生存和发展的最大威胁之一。因此,本文研究了一类考虑环境病毒影响的随机COVID-19传染病SEIW (W为病毒在环境中的浓度)模型是否存在平稳分布。首先,通过构造一个合适的Lyapunov函数证明了系统解的存在唯一性。然后利用随机Lyapunov方法建立了参数Rs0,并证明了当Rs0 >1时系统解在R4+上存在唯一的平稳分布。通过比较R0的确定性模型和R0的随机模型,可以发现,当σi→0 (i= 1,2,3,4), R0→R0时,R0受白噪声影响,且R0≤R0,说明本文的工作是对确定性模型的推广,当随机扰动较小时,系统解在R4+上存在唯一平稳分布。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stationary Distribution of a Random Epidemic Model with Virus Infection
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.
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