[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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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
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@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/
[1] Pneumonic plague pathogenesis and immunity in brown Norway rats, Am. J. Pathol., Volume 174 (2009) no. 3, pp. 910-921 | DOI
[2] The incubation period of cholera: A systematic review, J. Infect., Volume 66 (2013) no. 5, pp. 432-438 | DOI
[3] Un modèle mathématique des débuts de l’épidémie de coronavirus en France, Math. Model. Nat. Phenom., Volume 15 (2020), 29 | DOI
[4] Multiple casualty incidents: the prehospital role of the anesthesiologist in europe, Anesthesiology Clinics, Volume 25 (2007) no. 1, pp. 179-188 | DOI
[5] Ergodic behavior of non-conservative semigroups via generalized Doeblin’s conditione, Acta Appl. Math., Volume 166 (2020), pp. 29-72 | DOI | Zbl
[6] Curve fitting by segmented straight lines, J. Am. Stat. Assoc., Volume 64 (1969), pp. 1079-1084 | DOI | MR | Zbl
[7] Nonnegative matrices in the mathematical sciences, Computer Science and Applied Mathematics, Academic Press Inc., 1979 | Zbl
[8] Log-sum-exp neural networks and posynomial models for convex and log-log-convex data, IEEE Trans. Neural Netw. Learn. Syst., Volume 31 (2020) no. 3, pp. 827-838 | DOI | MR
[9] A time-dependent SIR model for COVID-19 with undetectable infected persons (2020) (https://arxiv.org/abs/2003.00122)
[10] Duality and separation theorems in idempotent semimodules, Linear Algebra Appl., Volume 379 (2004), pp. 395-422 | DOI | MR | Zbl
[11] Mathematical methods of statistics, Princeton Landmarks in Mathematics, 43, Princeton University Press, 1999 | Zbl
[12] Impact of lockdown on COVID-19 epidemic in Île-de-France and possible exit strategies, BMC Med, Volume 18 (2020), 240 | DOI
[13] Boundary theory of Markov processes (the discrete case, Russ. Math. Surv., Volume 24 (1969) no. 7, pp. 1-42 | DOI | MR | Zbl
[14] Coronavirus Covid 19 en Grand Est: Point de situation, 2020 (Press release of March 8th, available from https://www.grand-est.ars.sante.fr/system/files/2020-03/Covid19_point_GrandEst080320.pdf)
[15] Some remarks on changing populations, The Kinetics of Cellular Proliferation, Grune & Stratton, 1959, pp. 382-407
[16] Dobrushin’s ergodicity coefficient for Markov operators on cones, Integral Equations Oper. Theory, Volume 81 (2015) no. 1, pp. 127-150 | MR | Zbl
[17] Completely derandomized self-adaptation in evolution strategies, Evol. Comput., Volume 9 (2001) no. 2, pp. 159-195
[18] The medical response to multisite terrorist attacks in Paris, Lancet, Volume 386 (2015) no. 10012, pp. 2535-2538
[19] Ménages selon la taille en 2016. Comparaisons régionales et départementales, 2019 (https://www.insee.fr/fr/statistiques/2012714)
[20] Tropical algebraic geometry, Oberwolfach Seminars, 35, Birkhäuser, 2007 | MR | Zbl
[21] Continuous univariate distributions, Wiley Series in Probability and Mathematical Statistics, 1, John Wiley & Sons, 1994 | Zbl
[22] A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond., Ser. A, Volume 115 (1927), pp. 700-721 | Zbl
[23] Regression quantiles, Econometrica, Volume 46 (1978) no. 1, pp. 33-50 | DOI | MR | Zbl
[24] Convergence properties of the Nelder–Mead simplex method in low dimensions, SIAM J. Optim., Volume 9 (1998) no. 1, pp. 112-147 | DOI | MR | Zbl
[25] The incubation period of coronavirus disease 2019 (covid-19) from publicly reported confirmed cases: Estimation and application, Ann. Intern. Med., Volume 172 (2020) no. 9, pp. 577-582 | DOI
[26] Nonlinear Perron–Frobenius Theory, Cambridge Tracts in Mathematics, 189, Cambridge University Press, 2012 | MR | Zbl
[27] A covid-19 epidemic model with latency period, Infectious Disease Modelling, Volume 5 (2020), pp. 323-337
[28] Understanding unreported cases in the 2019-ncov epidemic outbreak in Wuhan, China, and the importance of major public health interventions, Biology, Volume 9 (2020) no. 3, 50, 12 pages
[29] Covid-19: Forecasting short term hospital needs in France (2020) (Report available in https://sfar.org/download/covid-19-forecasting-short-term-hospital-needs-in-france/)
[30] General relative entropy inequality: an illustration on growth models, J. Math. Pures et Appl., Volume 84 (2005) no. 9, pp. 1235-1260 | DOI | MR | Zbl
[31] Spectral analysis of semigroups and growth-fragmentation equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 33 (2016) no. 3, pp. 849-898 | DOI | MR | Zbl
[32] Weak Finsler structures and the Funk weak metric, Math. Proc. Camb. Philos. Soc., Volume 147 (2009) no. 2, pp. 419-437 | DOI | MR | Zbl
[33] Transport equations in biology, Frontiers in Mathematics, Birkhäuser, 2007 | Zbl
[34] Estimating the burden of SARS-CoV-2 in France, Science, Volume 369 (2020) no. 65000, pp. 208-211
[35] Données hospitalières relatives à l’épidémie de Covid-19 (https://www.data.gouv.fr/fr/datasets/donnees-hospitalieres-relatives-a-lepidemie-de-covid-19/, retrieved on May 10th, 2020)
[36] Bootstrap confidence intervals for the minimum sum of absolute errors regression, J. Stat. Comput. Simulation, Volume 48 (1993) no. 3-4, pp. 127-133
[37] Emergency calls are early indicators of ICU bed requirement during the COVID-19 epidemic (2020) (https://www.medrxiv.org/content/10.1101/2020.06.02.20117499v1.article-info, preprint)
[38] Investigation of a nosocomial outbreak of severe acute respiratory syndrome (SARS) in Toronto, Canada, CMAJ, Volume 169 (2003) no. 4, pp. 285-292
[39] Comparison of incubation period distribution of human infections with mers-cov in South Korea and Saudi Arabia, Sci. Rep., Volume 6 (2016), 35839, 7 pages
[40] Dequantization of real algebraic geometry on logarithmic paper, 3rd European congress of mathematics (ECM), Barcelona, Spain, July 10–14, 2000 (Carles et al. Casacuberta, ed.) (Progress in Mathematics), Volume 1, Birkhäuser, 2000, pp. 135-146 | Zbl
[41] Theory of Nonlinear Age-Dependent Population Dynamics, Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, 1985 | MR | Zbl
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