具有Ornstein-Uhlenbeck过程的随机SVI传染病模型的动力学行为研究OA
Dynamical Behavior of a Stochastic SVI Infectious Disease Model with Ornstein-Uhlenbeck Process
考虑到新生儿疫苗接种带来的社会效益和自然环境变化的不可预测性,本文引入Ornstein-Uhlenbeck过程来刻画传染率的随机波动,提出并研究一类随机SVI传染病模型.首先,分析证明模型全局正解的存在唯一性.其次,通过构造合适的Lyapunov函数和紧集,利用Itô公式等工具,证明模型平稳分布的存在性.此外,推导出传染病灭绝的充分条件.最后,通过数值模拟解释主要的理论结果.结果表明,提高疫苗接种率可有效遏制传染病的传播并降低传播风险,但无法完全消除传染病.
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.
曹虹;樊小琳;聂麟飞
新疆工程学院 数理学院,新疆 乌鲁木齐 830023||新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017新疆工程学院 数理学院,新疆 乌鲁木齐 830023新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830017
数理科学
Ornstein-Uhlenbeck过程SVI模型平稳分布灭绝性
Ornstein-Uhlenbeck processSVI modelstationary distributionextinction
《新疆大学学报（自然科学版中英文）》 2026 (3)
295-304,10
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)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)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).
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