基于分数阶导数的有效控制策略下病毒传播动力学的数学分析

IF 2.4 Q2 ENGINEERING, MECHANICAL
Rashid Jan, Normy Norfiza Abdul Razak, Salah Boulaaras, Ziad Ur Rehman, Salma Bahramand
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引用次数: 0

摘要

众所周知,病毒感染在多种方面对公共卫生产生重大影响,包括疾病负担、疫情和大流行、经济后果、应急响应、卫生保健系统压力、心理和社会影响以及疫苗接种的重要性。病毒感染的数学模型帮助决策者和研究人员了解疾病如何传播,预测干预措施的潜在影响,并做出明智的决定来控制和管理疫情。在这项工作中,我们在分数阶导数的框架下建立了COVID-19传播动力学的数学模型。对于推荐模型的分析,给出了基本概念和结果。为了模型的有效性,我们证明了推荐模型的解是正的和有界的。本研究对所提出的动力学进行了定性和定量分析。为了保证所提出的COVID-19动力学的存在唯一性,我们采用了Schaefer和Banach等不动点定理。除此之外,我们还通过数学技巧建立了COVID-19感染系统的稳定性结果。为了评估输入参数对感染动力学的影响,我们使用拉普拉斯阿多米安分解方法分析了解决途径。此外,我们进行了不同的模拟来概念化输入参数对感染动力学的作用。这些模拟提供了关键因素的可视化,并帮助公共卫生官员实施有效措施来控制病毒的传播。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mathematical analysis of the transmission dynamics of viral infection with effective control policies via fractional derivative
Abstract It is well known that viral infections have a high impact on public health in multiple ways, including disease burden, outbreaks and pandemic, economic consequences, emergency response, strain on healthcare systems, psychological and social effects, and the importance of vaccination. Mathematical models of viral infections help policymakers and researchers to understand how diseases can spread, predict the potential impact of interventions, and make informed decisions to control and manage outbreaks. In this work, we formulate a mathematical model for the transmission dynamics of COVID-19 in the framework of a fractional derivative. For the analysis of the recommended model, the fundamental concepts and results are presented. For the validity of the model, we have proven that the solutions of the recommended model are positive and bounded. The qualitative and quantitative analyses of the proposed dynamics have been carried out in this research work. To ensure the existence and uniqueness of the proposed COVID-19 dynamics, we employ fixed-point theorems such as Schaefer and Banach. In addition to this, we establish stability results for the system of COVID-19 infection through mathematical skills. To assess the influence of input parameters on the proposed dynamics of the infection, we analyzed the solution pathways using the Laplace Adomian decomposition approach. Moreover, we performed different simulations to conceptualize the role of input parameters on the dynamics of the infection. These simulations provide visualizations of key factors and aid public health officials in implementing effective measures to control the spread of the virus.
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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