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 .
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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provide an algorithm, based on
show that the logarithm of each epidemic observable can be approximated by
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approximation of the logarithm of epidemic observables,
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,
R
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
detect epidemic resurgences. We rely on a transport PDE epidemiological model, and we use methods from Perron-Frobenius theory and tropical geometry