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 Γ-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 numerical simulations are given according to the available data on Covid-19 epidemic in Italy.

Author information

Contact details are reproduced from the original publication and may be historical.

Lorenzo Freddi

Dip. di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, Udine, Italy

lorenzo.freddi@uniud.it

Dan Goreac

(1) School of Mathematics & Statistics, Shandong University, Weihai, P.R.China
(2) Université Gustave Eiffel, LAMA (UMR 8050), UPEM, UPEC, CNRS, Marne-la-Vallée, France

dan.goreac@univ-eiffel.fr

Keywords

  • Optimal control
  • SIR
  • Gamma-convergence
  • Pontryagin principle
  • state constraints
  • viability
  • epidemics
  • infinite horizon

Mathematics Subject Classification

49J45, 49K15, 49K21, 92D30

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Suggested citation

L. Freddi, D. Goreac. “Infinite Horizon Optimal Control of a SIR Epidemic Under an ICU Constraint.” Journal of Convex Analysis 31 (2024), No. 2, 525–562. https://doi.org/10.68381/jca31028

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