[Comprendre et surveiller l’évolution de l’épidémie de Covid-19 à partir des appels au numéro 15 : l’exemple de l’agglomération parisienne]
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.
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@article{CRMATH_2020__358_7_843_0,
author = {Gaubert, St\'ephane and Akian, Marianne and Allamigeon, Xavier and Boyet, Marin and Colin, Baptiste and Grohens, Th\'eotime and Massouli\'e, Laurent and Parsons, David P. and Adnet, Fr\'ed\'eric and Chanzy, \'Erick and Goix, Laurent and Lapostolle, Fr\'ed\'eric and Lecarpentier, \'Eric and Leroy, Christophe and Loeb, Thomas and Marx, Jean-S\'ebastien and T\'elion, Caroline and Tr\'eluyer, Laurent and Carli, Pierre},
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},
url = {http://www.numdam.org/articles/10.5802/crmath.99/}
}
TY - JOUR AU - Gaubert, Stéphane AU - Akian, Marianne AU - Allamigeon, Xavier AU - Boyet, Marin AU - Colin, Baptiste AU - Grohens, Théotime AU - Massoulié, Laurent AU - Parsons, David P. AU - Adnet, Frédéric AU - Chanzy, Érick AU - Goix, Laurent AU - Lapostolle, Frédéric AU - Lecarpentier, Éric AU - Leroy, Christophe AU - Loeb, Thomas AU - Marx, Jean-Sébastien AU - Télion, Caroline AU - Tréluyer, Laurent AU - Carli, Pierre TI - Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area JO - Comptes Rendus. Mathématique PY - 2020 SP - 843 EP - 875 VL - 358 IS - 7 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.99/ DO - 10.5802/crmath.99 LA - en ID - CRMATH_2020__358_7_843_0 ER -
%0 Journal Article %A Gaubert, Stéphane %A Akian, Marianne %A Allamigeon, Xavier %A Boyet, Marin %A Colin, Baptiste %A Grohens, Théotime %A Massoulié, Laurent %A Parsons, David P. %A Adnet, Frédéric %A Chanzy, Érick %A Goix, Laurent %A Lapostolle, Frédéric %A Lecarpentier, Éric %A Leroy, Christophe %A Loeb, Thomas %A Marx, Jean-Sébastien %A Télion, Caroline %A Tréluyer, Laurent %A Carli, Pierre %T Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area %J Comptes Rendus. Mathématique %D 2020 %P 843-875 %V 358 %N 7 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.99/ %R 10.5802/crmath.99 %G en %F CRMATH_2020__358_7_843_0
Gaubert, Stéphane; Akian, Marianne; Allamigeon, Xavier; Boyet, Marin; Colin, Baptiste; Grohens, Théotime; Massoulié, Laurent; Parsons, David P.; Adnet, Frédéric; Chanzy, Érick; Goix, Laurent; Lapostolle, Frédéric; Lecarpentier, Éric; Leroy, Christophe; Loeb, Thomas; Marx, Jean-Sébastien; Télion, Caroline; Tréluyer, Laurent; Carli, Pierre. Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area. Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 843-875. doi : 10.5802/crmath.99. http://www.numdam.org/articles/10.5802/crmath.99/
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