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

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  • Avram, Florin
  • Freddi, Lorenzo
  • Goreac, Dan

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.

Suggested Citation

  • Avram, Florin & Freddi, Lorenzo & Goreac, Dan, 2022. "Optimal control of a SIR epidemic with ICU constraints and target objectives," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008997
    DOI: 10.1016/j.amc.2021.126816
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    References listed on IDEAS

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    1. Fernando Alvarez & David Argente, 2020. "A Simple Planning Problem for COVID-19 Lockdown," Working Papers 2020-34, Becker Friedman Institute for Research In Economics.
    2. J. Frédéric Bonnans & Constanza Vega & Xavier Dupuis, 2013. "First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 1-40, October.
    3. Oluwaseun Sharomi & Tufail Malik, 2017. "Optimal control in epidemiology," Annals of Operations Research, Springer, vol. 251(1), pages 55-71, April.
    4. Thomas Kruse & Philipp Strack, 2020. "Optimal Control of an Epidemic through Social Distancing," Cowles Foundation Discussion Papers 2229, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Novak, Andrej, 2023. "A nonlinear optimal control problem with an application to optimal dosing of cytotoxic drugs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Florin Avram & Lorenzo Freddi & Dan Goreac & Juan Li & Junsong Li, 2023. "Controlled Compartmental Models with Time-Varying Population: Normalization, Viability and Comparison," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1019-1048, September.
    3. Cacace, Simone & Oliviero, Alessio, 2024. "Reliable optimal controls for SEIR models in epidemiology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 523-542.

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