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arXiv · 2306.10513

Infinite horizon optimal control of a SIR epidemic under an ICU constraint

Lorenzo Freddi·Dan Goreac
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Abstract

The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective functional linearly depends on the state and the control. After preliminary asymptotic and viability analyses, a $\Gamma$-convergence argument is developed to reduce the problem to a finite horizon allowing to use a state constrained version of Pontryagin's theorem to characterize the structure of the optimal controls. Illustrating examples and numeric simulations are given according to the available data on Covid-19 epidemic in Italy.

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Lorenzo Freddi, Dan Goreac. 2023-06-18. Infinite horizon optimal control of a SIR epidemic under an ICU constraint. https://arxiv.org/abs/2306.10513

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