视幂律内核中 SEIR 修正拉沙热模型的全局稳定性、Lyapunov 函数和动态性

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-02-12 DOI:10.1155/2024/3562684
Muhammad Farman, Cicik Alfiniyah, Muhammad Saqib
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引用次数: 0

摘要

拉沙热是一种影响人类的急性病毒性出血性疾病,在西非多个国家流行。本研究利用卡普托算子为 SEIR 型拉沙热传播(包括控制策略)构建了一个分数阶模型。所提出的模型研究了拉沙热从啮齿动物到人类、从人到人的传播动态,以及在社会中的感染区域。我们对模型进行了定性和定量分析。我们研究了正向不变区域,并展示了模型的正向有界解。我们还展示了感染发生和消亡的平衡状态。我们验证了所提出的非线性系统的存在,并利用定点定理证明了唯一解的存在。利用 Volterra 型 Lyapunov 函数,我们研究了带有分数卡普托导数的建议系统的全局稳定性。为了通过计算模拟研究分数算子的影响,我们在幂律核的广义版本中使用了两步拉格朗日多项式来生成结果。提供的图形评估显示了模型的简易性和可靠性,以及所有可能成为生态研究中重要病毒源的啮齿类动物。根据对不同分数阶次结果的比较,数值等于 1 的结论更有说服力。研究显示,如果考虑到所有传播方式,拉沙热的不利影响就会增加,而分数阶的结果表明对特定传播途径的不利影响较小。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global Stability with Lyapunov Function and Dynamics of SEIR-Modified Lassa Fever Model in Sight Power Law Kernel

Lassa fever is an acute viral hemorrhagic disease that affects humans and is endemic in various West African nations. In this study, a fractional-order model is constructed using the Caputo operator for SEIR-type Lassa fever transmission, including the control strategy. The proposed model examines the dynamics of Lassa fever transmission from rodents to humans and from person to person and in territories with infection in society. The model is analyzed both qualitatively and quantitatively. We examine the positively invariant area and demonstrate positive, bounded solutions to the model. We also show the equilibrium states for the occurrence and extinction of infection. The proposed nonlinear system is verified to be present, and a unique solution is shown to exist using fixed point theorems. Using the Volterra-type Lyapunov function, we investigate the global stability of the suggested system with a fractional Caputo derivative. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version of the power law kernel. A graphical evaluation is provided to show the simplicity and dependability of the model, and all rodents that could be source viruses are important in ecological research. The findings with a value equal to 1 are stronger, according to the comparison of outcomes with different fractional orders. The adverse effect of Lassa fever increases when all modes of transmission are taken into account, according to the study, with fractional-order findings indicating less detrimental effects on specific transmission routes.

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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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