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.
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.
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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
@article{CRMATH_2020__358_7_843_0, 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}, }
TY - JOUR AU - Stéphane Gaubert AU - Marianne Akian AU - Xavier Allamigeon AU - Marin Boyet AU - Baptiste Colin AU - Théotime Grohens AU - Laurent Massoulié AU - David P. Parsons AU - Frédéric Adnet AU - Érick Chanzy AU - Laurent Goix AU - Frédéric Lapostolle AU - Éric Lecarpentier AU - Christophe Leroy AU - Thomas Loeb AU - Jean-Sébastien Marx AU - Caroline Télion AU - Laurent Tréluyer AU - Pierre Carli 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 DO - 10.5802/crmath.99 LA - en ID - CRMATH_2020__358_7_843_0 ER -
%0 Journal Article %A Stéphane Gaubert %A Marianne Akian %A Xavier Allamigeon %A Marin Boyet %A Baptiste Colin %A Théotime Grohens %A Laurent Massoulié %A David P. Parsons %A Frédéric Adnet %A Érick Chanzy %A Laurent Goix %A Frédéric Lapostolle %A Éric Lecarpentier %A Christophe Leroy %A Thomas Loeb %A Jean-Sébastien Marx %A Caroline Télion %A Laurent Tréluyer %A Pierre Carli %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 %R 10.5802/crmath.99 %G en %F CRMATH_2020__358_7_843_0
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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