Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||42|
|Published online||30 November 2020|
COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability*
Faculté des Sciences, Université du Québec à Montréal (UQAM),
2 LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, 77454 Marne-la-Vallée, France.
3 ORFE Department, Princeton University, Princeton, USA.
** Corresponding author: firstname.lastname@example.org
Accepted: 3 November 2020
An extended SIR model, including several features of the recent COVID-19 outbreak, is considered: the infected and recovered individuals can either be detected or undetected and we also integrate an intensive care unit (ICU) capacity. We identify the optimal policy for controlling the epidemic dynamics using both lockdown and detection intervention levers, and taking into account the trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. With parametric specification based on the COVID-19 literature, we investigate the sensitivities of various quantities on the optimal strategies. The optimal lockdown policy is structured into 4 phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario avoids the second wave of infection, provided the lockdown is released sufficiently slowly. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.
Mathematics Subject Classification: 49N90 / 92D30 / 34H05
Key words: Optimal control / lockdown / testing / intensive care units / SARS-CoV-2
The authors thank Hélène Guérin, Olivier l’Haridon, Olivier Pietquin and Gabriel Turinici for stimulating discussions and feed-backs on early versions of that work, as well as participants of the Machine Learning Paris seminar, of the European Network for Business and Industrial Statistics (ENBIS) seminar, as well as participants of the working group at CMAP, École Polytechnique. R.E. and V.C.T. are partly supported by the Bézout Labex (ANR-10-LABX-58). V.C.T. is also part of ANR Cadence (ANR-16-CE32-0007), by the Chair “Modélisation Mathématique et Biodiversité” of Veolia Environnement-Ecole Polytechnique-Museum National d’Histoire Naturelle-Fondation X. A.C. gratefully acknowledges funding from NSERC grant 07077.
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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