一类带Lévy跳的随机SEIQR传染病模型动力学分析  

Dynamic Analysis of Stochastic SEIQR Epidemic Model with Lévy Jumps

作　　者：李晓岚 郭英佳[1] LI Xiaolan;GUO Yingjia(School Mathematics and Staistics,Beihua University,Jilin 132013,Jilin Province,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2023年第3期517-524,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12001017);北华大学研究生创新计划项目(批准号:北华研创合字[2021]039号);北华大学青年科研创新团队培育计划项目.

摘　　要：考虑不连续噪声对具有潜伏期疾病传播过程的影响,建立一类由Lévy噪声驱动的随机SEIQR传染病模型.先基于随机微分方程的相关理论,利用Lyapunov分析法证明随机SEIQR传染病模型全局正解的存在唯一性;然后通过构造恰当的Lyapunov函数,分别讨论该随机系统的解在相应确定性模型的无病平衡点和地方病平衡点处的渐近行为.We considered the influence of discontinuous noise on the disease transmission process with an incubation period,and established a stochastic SEIQR epidemic model driven by Lévy noise.Based on the relevant theory of stochastic differential equations,we proved the existence and uniqueness of the global positive solution of the stochastic SEIQR epidemic model by using the Lyapunov analysis method,and discussed the asymptotic behavior of the solutions for stochastic system at the disease-free equilibrium point and the endemic equilibrium point of the corresponding deterministic model respectively by constructing the appropriate Lyapunov functions.

关 键 词：Lévy噪声 随机SEIQR传染病模型 LYAPUNOV函数 正解存在唯一性 渐近行为 

分 类 号：O211.63[理学—概率论与数理统计]