The Dynamical Behaviors of a Stochastic Mumps Infectious Disease Model

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-01-05 DOI:10.1002/mma.10660

Suping Zhang, Feng Yang, Xiuyang Wu

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引用次数: 0

Abstract

The study of infectious disease dynamics plays an important role in reflecting the transmission mechanisms of epidemics. Compared with the traditional statistical methods, understanding dynamics of an infectious disease can better make people understand some global characteristics of epidemic and help in designing appropriate strategies to control diseases. Early studies of mumps mainly focused on deterministic models. However, environmental noises are inevitable during the spread of infectious diseases. This paper extends a mumps transmission model from a deterministic to a stochastic framework and explores the dynamical behaviors of the model by constructing suitable Lyapunov functions. Our model is a six-dimensional stochastic model. The construction of suitable Lyapunov functions is very challenging. Firstly, we show that this model has a unique global positive solution for any positive initial values. Secondly, we compute the basic reproduction numbers and present sufficient conditions for the existence of a unique ergodic stationary distribution and the extinction of the disease. Finally, we perform numerical simulations and sensitivity analysis for exploring the effect of some parameters and the white noises on the behavior of the model. The theoretical results can provide necessary guidelines to public health administrators for controlling and preventing diseases.

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随机流行性腮腺炎传染病模型的动力学行为

传染病动力学的研究对反映流行病的传播机制具有重要作用。与传统的统计方法相比，了解传染病的动态可以使人们更好地了解流行病的一些全球特征，有助于制定适当的疾病控制策略。流行性腮腺炎的早期研究主要集中在确定性模型上。然而，在传染病传播过程中，环境噪声是不可避免的。本文将流行性腮腺炎传播模型从确定性框架扩展到随机框架，并通过构造合适的Lyapunov函数来探讨模型的动力学行为。我们的模型是一个六维随机模型。构造合适的李雅普诺夫函数是非常具有挑战性的。首先，我们证明了该模型对于任何正初值都有唯一的全局正解。其次，我们计算了该疾病的基本繁殖数，并给出了唯一遍历平稳分布存在和疾病灭绝的充分条件。最后，进行了数值模拟和灵敏度分析，探讨了一些参数和白噪声对模型行为的影响。理论研究结果可为公共卫生管理者控制和预防疾病提供必要的指导。

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.