Extinction, Ultimate Boundedness, and Persistence in the Mean of a Stochastic Heroin Epidemic Model With Distributed Delay

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-19 DOI:10.1002/mma.10698

Xiaofeng Zhang

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引用次数: 0

Abstract

In this paper, we consider a stochastic heroin epidemic model with distributed delay. We analyze the model in detail: We prove the existence and uniqueness of the global positive solution of the system, the asymptotic behavior around the equilibrium point $E_{0}$ of the deterministic system, the stochastically ultimate boundedness, and the persistence in the mean of the disease. Finally, we verify the main conclusions of this paper through numerical simulation and explore the influence of system parameters on the persistence and extinction of diseases. According to the numerical simulation results, we can give some suggestions on controlling diseases.

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在本文中，我们考虑了一种具有分布式延迟的随机海洛因流行病模型。我们对模型进行了详细分析：我们证明了系统全局正解的存在性和唯一性、确定性系统在均衡点 E 0 $$ {E}_0 $$ 附近的渐近行为、随机终极有界性以及疾病均值的持续性。最后，我们通过数值模拟验证了本文的主要结论，并探讨了系统参数对疾病持续和消亡的影响。根据数值模拟结果，我们可以给出一些控制疾病的建议。

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.