A Novel Stochastic Model for Human Norovirus Dynamics: Vaccination Impact with Lévy Noise

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2024-06-12 DOI:10.3390/fractalfract8060349

Yuqin Song, Peijiang Liu, Anwarud Din

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引用次数: 0

Abstract

The epidemic norovirus causes vomiting and diarrhea and is a highly contagious infection. The disease is affecting human lives in terms of deaths and medical expenses. This study examines the governing dynamics of norovirus by incorporating Lévy noise into a stochastic SIRWF (susceptible, infected, recovered, water contamination, and food contamination) model. The existence of a non-negative solution and its uniqueness are proved after model formulation. Subsequently, the threshold parameter is calculated, and this number is used to explore the conditions under which disease tends to exist in the population. Likewise, additional conditions are derived that ensure the elimination of the disease from the community. It is proved that the norovirus is extinct whenever the threshold parameter is less than one and it persists for Rs>1. The work assumes two working examples to numerically explain the theoretical findings. Simulations of the study are visually presented, and comparisons are made. The results of this study suggest a robust approach for handling complex biological and epidemic phenomena.

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人类诺如病毒动态的新型随机模型：带有莱维噪声的疫苗接种影响

流行性诺如病毒会引起呕吐和腹泻，是一种传染性极强的传染病。这种疾病在死亡人数和医疗费用方面影响着人类的生活。本研究通过在随机 SIRWF（易感者、感染者、康复者、水污染和食物污染）模型中加入 Lévy 噪声，研究了诺如病毒的支配动力学。模型建立后，证明了非负解的存在及其唯一性。随后，计算出阈值参数，并利用该参数探索疾病在人群中趋于存在的条件。同样，还得出了确保疾病从群体中消除的附加条件。结果证明，只要阈值参数小于 1，诺如病毒就会灭绝，并且在 Rs>1 的条件下，诺如病毒会持续存在。该研究假设了两个工作实例，以数字形式解释理论发现。研究的模拟结果直观呈现，并进行了比较。研究结果为处理复杂的生物和流行病现象提供了一种稳健的方法。

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

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.