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
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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.
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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。
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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.
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