离散时间Sir流行病模型的输出轨迹可控性

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2023-04-24 DOI:10.1051/mmnp/2023015

Lahbib Benahmadi, M. Lhous, A. Tridane, M. Rachik

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引用次数: 0

摘要

摘要开发有助于控制传染病传播的新方法是公共卫生的一个关键问题。这种方法必须考虑到现有的资源和卫生保健系统的能力。本文通过研究最优控制问题，提出了一种新的控制流行病模型的数学方法，其目的是使流行病的输出达到目标期望的疾病输出yd = (yid)i∈{0，…，N}。首先，利用状态空间技术将轨迹可控性转化为具有最终状态约束的最优控制。然后，利用不动点定理确定可容许控制集，求解输出轨迹可控性问题。最后，我们将我们的方法应用于麻疹流行模型，并给出了数值模拟来说明我们的方法的发现。数学学科分类。-请给出AMS分类代码-。

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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OUTPUT TRAJECTORY CONTROLLABILITY OF A DISCRETE-TIME SIR EPIDEMIC MODEL

Abstract. Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease output yd = (yid)i∈{0,...,N}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach. Mathematics Subject Classification. — Please, give AMS classification codes —.

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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.