Optimal epidemic suppression under an ICU constraint: an analytical solution

Laurent Miclo (), Daniel Spiro and Jörgen Weibull
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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

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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.

Date: 2022
Note: View the original document on HAL open archive server: https://hal.science/hal-02563023v2
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Published in Journal of Mathematical Economics, 2022, 101, pp.102669. ⟨10.1016/j.jmateco.2022.102669⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02563023

DOI: 10.1016/j.jmateco.2022.102669

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