A SIQRB delayed model for cholera and optimal control treatment

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2022-06-25 DOI:10.1051/mmnp/2022027

Ana P. Lemos-Paião, H. Maurer, Cristiana J. Silva, Delfim F. M. Torres

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引用次数: 4

Abstract

We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.

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霍乱SIQRB延迟模型及其最优控制治疗

我们改进了最近的霍乱数学模型，增加了一个时间延迟，该时间延迟表示一个人被感染的时刻和他开始出现霍乱症状的时刻之间的时间。我们证明了延迟霍乱模型具有生物学意义，并分析了正时滞平衡点的局部渐近稳定性。提出并分析了一个最优控制问题，其目标是通过隔离获得最优治疗策略，以最大限度地减少感染个体的数量、细菌浓度以及治疗成本。将必要的最优性条件应用于具有$L^1$型成本函数的延迟最优控制问题。我们表明，与非延迟模型相比，延迟霍乱模型更适合2010年11月1日至2011年5月1日发生在海地阿蒂博尼特省的霍乱疫情。考虑到海地霍乱疫情的数据，我们对延迟最优控制问题进行了数值求解，并提出了控制和根除霍乱疫情的解决方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.