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

Abstract

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

CLC Number:

O175.13

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.

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References 22

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

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[3]	Yanjun Zhao,Xiaohui Sun,Li Su,Wenxuan Li. Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1861-1872.