Optimal control of a SIR epidemic with ICU constraints and target objectives

被引：23

作者：

Avram, Florin ^{[1
]}

Freddi, Lorenzo ^{[2
]}

Goreac, Dan ^{[3
,4
]}

机构：

[1] Univ Pau, Lab Math Appl, F-64012 Pau, France

[2] Dipartimento Sci Matemat Informat & Fis, Via Sci 206, I-33100 Udine, Italy

[3] Shandong Univ, Sch Math & Stat, Weihai 264209, Weihai, Peoples R China

[4] Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, LAMA,UPEM, F-77447 Marne La Valleee, France

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 418卷

关键词：

Optimal control; SIR; Pontryagin principle; State constraints; Viability; Epidemics; Feedback control;

D O I：

10.1016/j.amc.2021.126816

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and strict target objectives (related to the immunity threshold). The first class of results provides a comprehensive description of different zones of interest using viability tools. The second achievement is a thorough mathematical analysis of Pontryagin extremals for the aforementioned problem allowing to obtain an explicit closed-loop feedback optimal control. All our theoretical results are numerically illustrated for a further understanding of the geometrical features and scenarios. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：22

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[2]

ANDERSON R M, 1991

[3]

Aubin J.-P., 2009, VIABILITY THEORY, DOI [10.1007/978-0-8176-4910-4_1, DOI 10.1007/978-0-8176-4910-4_1]

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