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

Florin Avram, Lorenzo Freddi and Dan Goreac

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: 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.

Keywords: Optimal control; SIR; Pontryagin principle; State constraints; Viability; Epidemics; Feedback control (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008997

DOI: 10.1016/j.amc.2021.126816

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