  The first cases of COVID-19 in France were detected on January 24, 2020. The
number of screening tests carried out and the methodology used to target the
patients tested do not allow for a direct computation of the real number of
cases and the mortality rate.In this report, we develop a
'mechanistic-statistical' approach coupling a SIR ODE model describing the
unobserved epidemiological dynamics, a probabilistic model describing the data
acquisition process and a statistical inference method. The objective of this
model is not to make forecasts but to estimate the real number of people
infected with COVID-19 during the observation window in France and to deduce
the mortality rate associated with the epidemic.Main results. The actual number
of infected cases in France is probably much higher than the observations: we
find here a factor x 15 (95%-CI: 4-33), which leads to a 5.2/1000 mortality
rate (95%-CI: 1.5 / 1000-11.7/ 1000) at the end of the observation period. We
find a R0 of 4.8, a high value which may be linked to the long viral shedding
period of 20 days.

Populations and Evolution;Dynamical Systems;Applications