Lévy 噪声驱动下基于 Logistic 增长和心理效应的随机 SIQS 传染病模型

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2397-2417.

Lévy 噪声驱动下基于 Logistic 增长和心理效应的随机 SIQS 传染病模型

赵彦军¹^,^*(), 霍灵光¹, 苏丽¹, 孙晓辉¹, 李文轩²

¹ 吉林外国语大学国际组织研究院, 国际金融与贸易学院长春 130117
² 吉林大学数学学院长春 130012

收稿日期:2025-08-26 修回日期:2025-12-12 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 赵彦军 E-mail:zhaoyanjun@jisu.edu.cn
基金资助:
国家自然科学基金(11271154);吉林省教育厅科学技术研究项目(JJKH20261137KJ);吉林外国语大学 2025 年度校级科研重点项目(JW2025ZDB004)

A Stochastic SIQS Epidemic Model Driven by Lévy Noise with Logistic Growth and Psychological Effects

Yanjun Zhao¹^,^*(), Lingguang Huo¹, Li Su¹, Xiaohui Sun¹, Wenxuan Li²

¹ Research Institute for International Organizations and School of International Finance and Trade, Jilin International Studies University, Changchun 130117
² College of Mathematics, Jilin University, Changchun 130012

Received:2025-08-26 Revised:2025-12-12 Online:2026-12-26 Published:2026-08-14
Contact: Yanjun Zhao E-mail:zhaoyanjun@jisu.edu.cn
Supported by:
NSFC(11271154);Scientific and Technological Research Project of the Education Department of Jilin Province(JJKH20261137KJ);2025 Key University-Level Scientific Research Project of Jilin International Studies University(JW2025ZDB004)

摘要/Abstract

摘要：

该文研究了一类 Lévy 噪声驱动下基于 Logistic 增长和心理效应的随机 SIQS 传染病模型. 首先, 通过构造 Lyapunov 函数并利用 $\rm It\hat{o}$ 公式, 证明了模型全局正解的存在唯一性. 其次, 研究了该模型分别在相应确定性模型的无病平衡点以及地方病平衡点附近解的渐近性质. 再次, 定义随机 SIQS 模型的基本再生数 $R_{0}^{s}$, 在一定的条件下, 借助 $R_{0}^{s}$ 和利用 $\rm It\hat{o}$ 公式得到了疾病灭绝与持久的充分性条件. 最后, 通过数值模拟验证了理论分析结果的正确性.

关键词: Lévy 噪声, Logistic 增长, 心理效应, 渐近性质, 灭绝与持久

Abstract:

A class of stochastic SIQS epidemic model driven by Lévy noise with Logistic growth and psychological effects is investigated. Firstly, the existence and uniqueness of the global positive solution of the model are proved by constructing Lyapunov function and applying $\rm It\hat{o}'s$ formula. Secondly, the asymptotic properties of the stochastic model at the disease-free equilibrium point and the endemic equilibrium point of the corresponding deterministic model are analyzed. Thirdly, the stochastic basic reproduction number $R_{0}^{s}$ is defined for the stochastic SIQS model. Under certain conditions, sufficient criteria for disease extinction and persistence are established by leveraging $R_{0}^{s}$ and $\rm It\hat{o}'s$ formula. Finally, the correctness of the theoretical analysis results is verified by numerical simulation.

Key words: Lévy noise, logistic growth, psychological effect, asymptotic properties, extinction and persistence

中图分类号:

O175.13

赵彦军, 霍灵光, 苏丽, 孙晓辉, 李文轩. Lévy 噪声驱动下基于 Logistic 增长和心理效应的随机 SIQS 传染病模型[J]. 数学物理学报, 2026, 46(6): 2397-2417.

Yanjun Zhao, Lingguang Huo, Li Su, Xiaohui Sun, Wenxuan Li. A Stochastic SIQS Epidemic Model Driven by Lévy Noise with Logistic Growth and Psychological Effects[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2397-2417.

图/表 4

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