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Optimal epidemic suppression under an ICU constraint: an analytical solution

Author

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  • Laurent Miclo

    (IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique, TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Daniel Spiro

    (Uppsala University)

  • Jörgen Weibull

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris, SSE/ECON - Department of Economics, Stockholm School of Economics - SSE - Stockholm School of Economics)

Abstract
How much and when should we limit economic and social activity to ensure that the health-care system is not overwhelmed during an epidemic? We study a setting where ICU resources are constrained while suppression is costly (e.g., limiting economic interaction). Providing a fully analytical solution we show that the common wisdom of "flattening the curve", where suppression measures are continuously taken to hold down the spread throughout the epidemic, is suboptimal. Instead, the optimal suppression is discountinuous. The epidemic should be left unregulated in a first phase and when the ICU constraint is approaching society should quickly lock down (a discontinuity). After the lockdown regulation should gradually be lifted, holding the rate of infected constant thus respecting the ICU resources while not unnecessarily limiting economic activity. In a final phase, regulation is lifted. We call this strategy "filling the box". * We wish to thank Tommy Andersson, Hannes Malmberg and Robert Östling for valuable comments.

Suggested Citation

  • Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2022. "Optimal epidemic suppression under an ICU constraint: an analytical solution," Post-Print hal-02563023, HAL.
    • Handle: RePEc:hal:journl:hal-02563023
    DOI: 10.1016/j.jmateco.2022.102669
    Note: View the original document on HAL open archive server: https://hal.science/hal-02563023v2
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    References listed on IDEAS

    as
    1. Christian Gollier, 2020. "Cost–benefit analysis of age‐specific deconfinement strategies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(6), pages 1746-1771, December.
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    5. Gonzalez-Eiras, Martin & Niepelt, Dirk, 2020. "On the Optimal "Lockdown" During an Epidemic," CEPR Discussion Papers 14612, C.E.P.R. Discussion Papers.
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    9. Miclo, Laurent & Weibull, Jörgen W. & Spiro, Daniel, 2020. "Optimal epidemic suppression under an ICU constraint," TSE Working Papers 20-1111, Toulouse School of Economics (TSE).
    10. David Berger & Kyle Herkenhoff & Chengdai Huang & Simon Mongey, 2022. "Testing and Reopening in an SEIR Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 1-21, January.
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    13. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
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    Cited by:

    1. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Sun, Rui & Zhao, Yikai, 2023. "Intervention uncertainty, household health, and pandemic," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    3. Hubert Kempf & stéphane Rossignol, 2023. "Lockdown policies and the dynamics of a pandemic: foresight, rebounds and optimality," Documents de recherche 23-06, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    4. Mart n Gonzales-Eiras, Dirk Niepelt, 2023. "Optimal Epidemic Control," Diskussionsschriften dp2311, Universitaet Bern, Departement Volkswirtschaft.

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