Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2020-11-01 DOI:10.5556/j.tkjm.51.2020.2860
Shaibu Osman, O. Makinde, D. Theuri
{"title":"Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.","authors":"Shaibu Osman, O. Makinde, D. Theuri","doi":"10.5556/j.tkjm.51.2020.2860","DOIUrl":null,"url":null,"abstract":"Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"96 1","pages":"261-287"},"PeriodicalIF":0.7000,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.51.2020.2860","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 13

Abstract

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
最优控制下动物和人类李斯特菌病流行的数学模型。
李斯特菌病是由单核增生李斯特菌引起的一种严重疾病。人们通常在食用包括肉类在内的受污染的食物后患上李斯特菌病。这种疾病主要影响孕妇、新生儿、老年人和免疫系统较弱的人。本文利用微分方程的稳定性理论,提出并研究了李斯特菌病在动物和人群中的传播动力学模型问题。从无病平衡点和地方病平衡点的稳定性出发,定性地分析了该模型的基本繁殖数以及向前和向后分叉的可能性。通过敏感性分析评估模型参数对疾病的影响。对模型进行了扩展,以包括时间相关的控制变量,如治疗、疫苗接种和易感(人)的教育。利用庞特里亚金的极大值原理,我们得到了对抗李斯特菌病所需的最优控制策略。对该模型进行了数值模拟,并对相关结果进行了图形化显示和定量讨论。
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 去求助
来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
期刊最新文献
Various new traveling wave solutions for conformable time-fractional Sasa-Satsuma equation Common solutions of fixed point and generalized equilibrium problems using asymptotically nonexpansive mapping Mathematical modeling and optimal control of a deterministic SHATR model of HIV/AIDS with possibility of rehabilitation: a dynamic analysis Some fixed point results for nonlinear $F$-type contractions in strong partial b-metric spaces $n$-harmonicity, minimality, conformality and cohomology
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1