Forecasting the local progression of the Covid-19 epidemic from medical emergency calls: the example of the Paris area

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 provide an algorithm, based on a piecewise linear approximation of the logarithm of epidemic observables, allowing one to monitor the epidemic. Our methods combine ideas from several fields of mathematics: tropical geometry, Perron--Frobenius theory, probability and optimization, transport PDE in population dynamics.