莱维噪声下霍乱流行病非线性随机模型的动力学特性

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2024-05-16 DOI:10.3390/fractalfract8050293
Q. Ain, Anwarud Din, Xiaoli Qiang, Zheng Kou
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引用次数: 0

摘要

在本研究中,我们建立了一个综合数学模型来分析流行性霍乱的动态变化,其特点是由于病原体在人体内过量而导致急性腹泻。该模型首先从确定性角度出发,然后通过随机微分方程将随机性纳入其中。研究选择了莱维噪声,而不是其他众所周知的噪声类型,强调了其在流行病建模中的重要性。除了提出随机系统的生物学理由外,我们还证明了等效的确定性模型显示了可能的均衡。介绍之后是对模型的理论分析。通过严格的分析,我们确定了随机模型确保了唯一的全局解。我们应用李亚普诺夫函数理论构建了必要条件,这些条件平均保证了模型在 R0s>1 时的稳定性。我们的研究结果表明,当 Rs 小于 1 时,根除疾病的可能性很大,模型的图形模拟支持了这一重要见解。为了提高分析结果的稳健性,我们通过模拟模型生成了图形图解。这项工作为彻底理解一系列此类疾病提供了强有力的理论框架。这项研究不仅加深了对霍乱动力学的理解,还提供了一个适用于一系列类似疾病的稳健理论框架,以及一种为具有随机扰动的非线性模型构建 Lyapunov 函数的新方法。
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Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise
In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
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