Infinite horizon optimal control of a SIR epidemic under an ICU constraint
Optimization and Control
2024-03-12 v2
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 -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.
Keywords
Cite
@article{arxiv.2306.10513,
title = {Infinite horizon optimal control of a SIR epidemic under an ICU constraint},
author = {Lorenzo Freddi and Dan Goreac},
journal= {arXiv preprint arXiv:2306.10513},
year = {2024}
}