  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.
