Asymptotic Properties of a Stochastic SIR Model With Regime Switching and Mean-Reverting Ornstein–Uhlenbeck Process

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-06 DOI:10.1002/mma.10875

Wei Wei, Wei Xu, Deli Wang

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引用次数: 0

Abstract

The goal of this paper is to investigate a new mean-reverting Ornstein–Uhlenbeck process based stochastic SIR model with regime switching for diseases transmission that still is a threat to human health and life. In this paper, the deterministic model is extended to the stochastic switched form by incorporating the Ornstein–Uhlenbeck process and Markov switching to account the environmental noise. Firstly, with the Lyapunov functions, the existence of global unique positive solution is proved. Then, the sufficient criteria that control the disease's extinction and persistence of the disease are identified through the Khasminskii theory and stochastic comparison theorem. Epidemiologically, it is found that the larger proportions of the intensity of volatility and the speed of reversion can suppress the outbreak of diseases. At last, numerical simulations are provided to verify our theoretical findings and study the effects of Markov switching and Ornstein–Uhlenbeck process on the spread of the disease.

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具有状态切换和均值恢复的随机SIR模型的渐近性质

本文的目的是研究一种新的基于均数恢复的Ornstein-Uhlenbeck过程的随机SIR模型，该模型具有状态切换，用于仍然威胁人类健康和生命的疾病传播。本文通过考虑环境噪声，结合Ornstein-Uhlenbeck过程和Markov转换，将确定性模型扩展为随机切换形式。首先，利用Lyapunov函数证明了全局唯一正解的存在性。然后，通过Khasminskii理论和随机比较定理，确定了控制疾病灭绝和疾病持续的充分准则。流行病学研究发现，较大比例的波动强度和逆转速度可以抑制疾病的爆发。最后通过数值模拟验证了我们的理论发现，并研究了马尔可夫转换和Ornstein-Uhlenbeck过程对疾病传播的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.