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

Abstract : The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics. The 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-03453722
Contributor : Dan Goreac Connect in order to contact the contributor
Submitted on : Sunday, November 28, 2021 - 5:44:15 PM
Last modification on : Friday, January 14, 2022 - 3:42:01 AM

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AFG_CtrlSIR_Rev2.pdf
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  • HAL Id : hal-03453722, version 1

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Florin Avram, Lorenzo Freddi, Dan Goreac. Optimal control of a SIR epidemic with ICU constraints and target objectives. Applied Mathematics and Computation, Elsevier, 2022, 418. ⟨hal-03453722⟩

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