Stability Analysis and Simulation of Diffusive Vaccinated Models

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Complexity Pub Date : 2024-10-11 DOI:10.1155/2024/5595996
Mohammed M. Al-Shamiri, N. Avinash, P. Chellamani, Manal Z. M. Abdallah, G. Britto Antony Xavier, V. Rexma Sherine, M. Abisha
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Abstract

This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease’s time transmission, it is important to examine the global stability of the equilibrium points. Disease-free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease-free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler’s approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission.

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扩散式疫苗接种模型的稳定性分析与模拟
本文首先分析了扩散接种模型的关键数学特性,包括存在性、唯一性、实在性和有界性。确定了均衡点,并计算了基本繁殖数。应用巴拿赫收缩映射原理严格确定了解的存在性和唯一性。为了了解疾病的时间传播,研究平衡点的全局稳定性非常重要。无疾病均衡和地方病均衡是该模型中的两个均衡点。在此,我们证明了当基本繁殖数大于 1 时,地方病平衡点是全局渐近稳定的,而当基本繁殖数小于 1 时,无病平衡点是全局渐近稳定的。此外,基于卡普托分数阶导数和隐式欧拉近似,我们为结果系统提供了无条件稳定的数值解。这项工作利用一种称为迭代拉普拉斯变换的方法,探索了一些非整数阶重要人口模型的求解方法。所提出的方法是将拉普拉斯变换与迭代程序有效结合。这样就可以得到一个向精确解收敛的序列形式解。我们注意到,所获得的解与精确解之间存在密切联系。此外,所建议的方法可以处理各种分数阶导数问题,因为它涉及的计算量极少。这些信息将有助于进一步研究确定预防或阻止疾病传播的理想行动策略。
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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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