新疆大学学报（自然科学版中英文）2026，Vol.43Issue(3)：295-304,10.DOI:10.13568/j.cnki.651094.651316.2025.08.29.0001
具有Ornstein-Uhlenbeck过程的随机SVI传染病模型的动力学行为研究
Dynamical Behavior of a Stochastic SVI Infectious Disease Model with Ornstein-Uhlenbeck Process
摘要
Abstract
Considering the great social benefits of vaccination and the unpredictability of changes in the natural environ-ment,this paper introduces the Ornstein-Uhlenbeck process to characterize the stochastic fluctuations in the transmission rate,proposes and studies a stochastic SVI epidemic model.Firstly,the existence and uniqueness of the global positive solution for the model are analyzed.Secondly,by constructing appropriate Lyapunov functions,defining a compact set,and using tools such as Itô's formula,the existence of a stationary distribution for the model is proved.In addition,the sufficient condition for disease extinction is derived.Finally,some numerical simulations are used to explain the main theoretical results.The re-sults show that,increasing vaccination rates can inhibit the rise in the number of infections and reduce the risk of transmis-sion,but it can not completely eliminate the disease.关键词
Ornstein-Uhlenbeck过程/SVI模型/平稳分布/灭绝性Key words
Ornstein-Uhlenbeck process/SVI model/stationary distribution/extinction分类
数理科学引用本文复制引用
曹虹,樊小琳,聂麟飞..具有Ornstein-Uhlenbeck过程的随机SVI传染病模型的动力学行为研究[J].新疆大学学报（自然科学版中英文）,2026,43(3):295-304,10.基金项目
新疆维吾尔自治区自然科学基金"几类具有Ornstein-Uhlenbeck过程的随机传染病模型研究"(2025D01B87) （2025D01B87）
新疆维吾尔自治区研究生科研创新项目"具有Black-Karasinski过程的随机传染病模型研究"(XJ2025G016) （XJ2025G016）
新疆大学优秀博士研究生创新项目"几类具有均值回归过程的随机传染病模型研究"(XJU2024BS046). （XJU2024BS046）
