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

Stéphane Gaubert; Marianne Akian; Xavier Allamigeon; Marin Boyet; Baptiste Colin; Théotime Grohens; Laurent Massoulié; David P. Parsons; Frédéric Adnet; Érick Chanzy; Laurent Goix; Frédéric Lapostolle; Éric Lecarpentier; Christophe Leroy; Thomas Loeb; Jean-Sébastien Marx; Caroline Télion; Laurent Tréluyer; Pierre Carli

doi:10.5802/crmath.99

Modélisation mathématique, Biomathématiques

Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area
[Comprendre et surveiller l’évolution de l’épidémie de Covid-19 à partir des appels au numéro 15 : l’exemple de l’agglomération parisienne]

Stéphane Gaubert ¹ ; Marianne Akian ² ; Xavier Allamigeon ¹ ; Marin Boyet ¹ ; Baptiste Colin ¹ ; Théotime Grohens ³ ; Laurent Massoulié ⁴ ; David P. Parsons ⁵ ; Frédéric Adnet ⁶ ; Érick Chanzy ⁷ ; Laurent Goix ⁷ ; Frédéric Lapostolle ⁸ ; Éric Lecarpentier ⁷ ; Christophe Leroy ⁷ ; Thomas Loeb ⁷ ; Jean-Sébastien Marx ⁷ ; Caroline Télion ⁷ ; Laurent Tréluyer ⁷ ; Pierre Carli ⁹

¹ INRIA, CMAP, École polytechnique, IP Paris, CNRS
² INRIA,CMAP, École polytechnique, IP Paris, CNRS
³ INRIA, Université de Lyon, CNRS, INSA-Lyon, LIRIS, UMR5205
⁴ INRIA, ENS, CNRS, PSL University, Microsoft Research-INRIA Joint Centre
⁵ INRIA
⁶ AP-HP, Université Paris XIII, Bobigny
⁷ AP-HP
⁸ AP-HP,Université Paris XIII, Bobigny
⁹ AP-HP, Université Paris-Descartes, Paris

Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 843-875.

Résumé
Abstract

Nous décrivons l’évolution de l’épidémie de Covid-19 dans l’agglomération parisienne, pendant la crise de Mars–Avril 2020, en analysant les appels d’urgence au numéro 15 traités par les SAMU des quatre départements centraux de l’agglomération (75, 92, 93 et 94). Notre étude révèle de fortes disparités entres ces départements. Nous montrons que le logarithme de toute observable épidémique peut être approché par une fonction du temps linéaire par morceaux. Cela nous permet d’identifier les différentes phases d’évolution de l’épidémie, et aussi d’évaluer le délai entre la prise de mesures sanitaires et leur effet sur la sollicitation de l’aide médicale urgente. Nous en déduisons un algorithme permettant de détecter une resurgence éventuelle de l’épidémie. Notre approche s’appuie sur un modèle d’EDP de transport de l’évolution épidémique, ainsi que sur des méthodes de théorie de Perron–Frobenius et de géométrie tropicale.

We portray the evolution of the Covid-19 epidemic during the crisis of March–April 2020 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. This 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. We rely on a transport PDE epidemiological model, and we use methods from Perron–Frobenius theory and tropical geometry.

Reçu le : 2020-06-10
Révisé le : 2020-07-20
Accepté le : 2020-07-21
Publié le : 2020-11-16

DOI : 10.5802/crmath.99

Affiliations des auteurs :

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {St\'ephane Gaubert and Marianne Akian and Xavier Allamigeon and Marin Boyet and Baptiste Colin and Th\'eotime Grohens and Laurent Massouli\'e and David P. Parsons and Fr\'ed\'eric Adnet and \'Erick Chanzy and Laurent Goix and Fr\'ed\'eric Lapostolle and \'Eric Lecarpentier and Christophe Leroy and Thomas Loeb and Jean-S\'ebastien Marx and Caroline T\'elion and Laurent Tr\'eluyer and Pierre Carli},
     title = {Understanding and monitoring the evolution of the {Covid-19} epidemic from medical emergency calls: the example of the {Paris} area},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {843--875},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {7},
     year = {2020},
     doi = {10.5802/crmath.99},
     language = {en},
}

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AU  - Jean-Sébastien Marx
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%A Thomas Loeb
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%A Laurent Tréluyer
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Stéphane Gaubert; Marianne Akian; Xavier Allamigeon; Marin Boyet; Baptiste Colin; Théotime Grohens; Laurent Massoulié; David P. Parsons; Frédéric Adnet; Érick Chanzy; Laurent Goix; Frédéric Lapostolle; Éric Lecarpentier; Christophe Leroy; Thomas Loeb; Jean-Sébastien Marx; Caroline Télion; Laurent Tréluyer; Pierre Carli. Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area. Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 843-875. doi : 10.5802/crmath.99. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.99/

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