An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

Chandrali Baishya, Sindhu J. Achar, P. Veeresha
{"title":"An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model","authors":"Chandrali Baishya, Sindhu J. Achar, P. Veeresha","doi":"10.37256/cm.5120242363","DOIUrl":null,"url":null,"abstract":"Vaccination programs aimed at preventing the spread of the coronavirus appear to have a significant global impact. In this research, we have investigated a mathematical model projecting COVID-19 disease spread by considering five groups of individuals viz. vulnerable, exposed, infected, unreported, recovered, and vaccinated. Looking at the current abnormal pattern of the virus spread in the projected model, we have implemented the fractional derivative in the Mittag-Leffler context. Using the existing theory of the fractional derivative, we have examined the theoretical aspects such as the existence and uniqueness of the solutions, the existence and stability of the disease-free and endemic equilibrium points, and the global stability of the disease-free equilibrium point. In computing the basic reproduction number, we have analyzed that the existence and stability of points of equilibrium are dependent on this number. The sensitivity of the basic reproduction number is also examined. The importance of the vaccination drive is highlighted by relating it to the basic reproduction number. Finally, we have presented the simulation of the numerical results by capturing the profile of each group under the influence of the fractional derivative and investigated the impact of vaccination rate and contact rate in controlling the disease by applying the Adams-Bashforth-Moultan (ABM) method. The present research study demonstrates the importance of the vaccination campaign and the curb on individual contact by featuring a novel fractional operator in the projected model and capturing the corresponding consequence.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contemporary Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37256/cm.5120242363","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

Vaccination programs aimed at preventing the spread of the coronavirus appear to have a significant global impact. In this research, we have investigated a mathematical model projecting COVID-19 disease spread by considering five groups of individuals viz. vulnerable, exposed, infected, unreported, recovered, and vaccinated. Looking at the current abnormal pattern of the virus spread in the projected model, we have implemented the fractional derivative in the Mittag-Leffler context. Using the existing theory of the fractional derivative, we have examined the theoretical aspects such as the existence and uniqueness of the solutions, the existence and stability of the disease-free and endemic equilibrium points, and the global stability of the disease-free equilibrium point. In computing the basic reproduction number, we have analyzed that the existence and stability of points of equilibrium are dependent on this number. The sensitivity of the basic reproduction number is also examined. The importance of the vaccination drive is highlighted by relating it to the basic reproduction number. Finally, we have presented the simulation of the numerical results by capturing the profile of each group under the influence of the fractional derivative and investigated the impact of vaccination rate and contact rate in controlling the disease by applying the Adams-Bashforth-Moultan (ABM) method. The present research study demonstrates the importance of the vaccination campaign and the curb on individual contact by featuring a novel fractional operator in the projected model and capturing the corresponding consequence.
卡普托分数域在 COVID-19 数学模型分析中的应用
旨在防止冠状病毒传播的疫苗接种计划似乎对全球产生了重大影响。在这项研究中,我们通过考虑易感人群、暴露人群、感染人群、未报告人群、康复人群和疫苗接种人群这五类人群,研究了预测 COVID-19 疾病传播的数学模型。针对预测模型中当前病毒传播的异常模式,我们在 Mittag-Leffler 背景下实现了分数导数。利用现有的分数导数理论,我们研究了解的存在性和唯一性、无疾病平衡点和流行平衡点的存在性和稳定性以及无疾病平衡点的全局稳定性等理论问题。在计算基本繁殖数时,我们分析了平衡点的存在性和稳定性取决于该数。我们还研究了基本繁殖数的敏感性。通过将疫苗接种驱动与基本繁殖数联系起来,突出了疫苗接种驱动的重要性。最后,我们通过捕捉分数导数影响下各群体的轮廓,对数值结果进行了模拟,并应用亚当斯-巴什福斯-穆尔坦(ABM)方法研究了疫苗接种率和接触率对控制疾病的影响。本研究通过在预测模型中采用新颖的分数算子并捕捉相应的结果,证明了疫苗接种活动和遏制个人接触的重要性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信