Session S15 - Mathematics of Planet Earth

Thursday, July 15, 16:00 ~ 16:25 UTC-3

Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area

Marianne AKIAN

Inria and CMAP, Ecole polytechnique, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will present a work done during the Covid-19 epidemic crisis of March–April 2020. We portray the evolution of the epidemic in the Paris area, by analyzing the medical emergency calls received by the EMS of the four central departments of this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between these departments. We show that the logarithm of each epidemic observable can be approximated by a piecewise linear function of time. Such an approximation allows us to distinguish the different phases of the epidemic, and to identify the delay between sanitary measures and their influence on the load of EMS. This also leads to an algorithm, allowing one to detect epidemic resurgences, by identifying nondifferentiability points.

Piecewise linearity is established from a transport PDE epidemiological model, using methods from Perron–Frobenius theory and tropical geometry. In order to compute a piecewise linear approximation, we minimize the $\ell^1$ norm of the error. This is done using a dynamic programming approach. We provide metric estimates showing that this method is robust with respect to perturbations of epidemic observables.

The main part of this work was done jointly by the following team of physicians of the SAMU of AP-HP and applied mathematicians from INRIA and École polytechnique: Stéphane Gaubert, Marianne Akian, Xavier Allamigeon, Marin Boyet, Baptiste Colin, Théotime Grohens, Laurent Massoulié, David P. Parsons, Frédéric Adnete, Érick Chanzy, Laurent Goix, Frédéric Lapostolle, Éric Lecarpentier, Christophe Leroy, Thomas Loeb, Jean-Sébastien Marx, Caroline Télion, Laurent Tréluyer, and Pierre Carli. It has been published in Comptes Rendus Mathématique, vol. 358, n7, p. 843-875, 2020.

The part on $\ell^1$ norm optimization is a joint work with Ayoub Foussoul, Jérôme Bolte, Stéphane Gaubert, and Laurent Massoulié.

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