一类具有 Lévy噪声的COVID-19传播动力学行为分析
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摘要：
随机扰动在传染病的传播过程中是不可避免的，为了研究这种扰动对COVID-19传播的影响，提出了一种同时具有白噪声和Lévy跳跃的随机SIVR(易感-感染-疫苗接种-康复) 流行病模型。首先，通过构造合适的李雅普诺夫函数，证明了全局正解的存在唯一性；然后，通过定义随机系统的阈值，得到了疾病的灭绝和持续存在的充分条件。最后，数值模拟验证了理论分析的结果，结果表明高强度的Lévy噪声有利于快速抑制COVID-19的传播。
Stochastic perturbations are inevitable in the transmission of infectious diseases. In order to examine the impact of disturbances on the spread of COVlD-19, a SlVR (Susceptibility-Infection- Vaccination-Recovery) epidemic model with Levy jumps as well as white noise is proposed in this paper, lnitially,the existence and uniqueness of the global positive solutior is proved by constructing a suitable lyapunov function. Then, sufficient conditions for the extinction and persistence of the disease are obtained by defining the thresholds of the stochastic system. Finally, numerical simulations verify the results of the theoretical analysis, and the results show that the high-intensity Lévy noise is conducive to suppressing the propagation of COVID-19 rapidly.
作者：
谭远顺，冉崇玉
Tan Yuanshun, Ran Chongyu
机构地区：
重庆交通大学数学与统计学院
引用本文：
谭远顺，冉崇玉。一类具有Lévy噪声的COVID-19传播动力学行为分析[J] . 学报(自然科学版), 2025,53(2) : 44-53. (Tan Yuanshun, Ran Chongyu. Behavioral analysis of a class of COVID-19 propagation dynamics with Lévy noise[J] . Journal of Henan Normal University(Natural Science Edition) , 2025, 53(2) : 44-53. DOI:10. 16366/j. cnki.1000-2367. 2023. 11. 30. 0005. )
基金：
国家自然科学基金；重庆市自然科学基金创新发展联合基金；重庆市研究生科研创新项目
关键词：
COVID-19；Lévy噪声；存在唯一性；灭绝性；持久性
COVID-19; Lévy noise; the existence and uniqueness; extinction; persistence
分类号：
O175
