Realistic estimate of the cumulative and instantaneous Covid-19 incidence in France

Malpuech, Guillaume

Based on a simple analysis of the reports of Sant\'e Public France, we show that the real incidence during the second wave of the Covid-19 outbreak is around 60% of the mean positivity of virological tests realized week after week in France. The fraction of the French population infected at the beginning of September is about 3% (2 million people). Both intensive care units (ICU) admission and death rate, which dropped by more than one order of magnitude since March, are currently 0.017% and 0.015% respectively. Simulations of the outbreak evolution based on the hypothesis of negligible reinfection probability are performed for France, Ile de France, Puy de Dome and Bouches du Rhone. The incidence peak of 3.5 % is expected at week 39 for France. These values are 4.5 % at week 37 for Ile de France (for which the peak already passed), 4.2 % at weeks 41-42 for Puy de Dome, 7% at week 38 for Bouches du Rhone. The calculated total number of ICU admission and deaths during the second wave are both found around 3000. The cumulative incidence over the two waves is computed close to 50 % for France and 80 % for Ile de France. We conclude that Covid-19 is much more spread than previously thought, but its severity became very limited since the end of the first wave. The level of spreading raises doubts in the large-scale testing strategy which anyway detects only a few percents of infected people. It also raises doubts in the efficiency of the closing of school classes, where a pupil is tested Covid-positive by chance. Finally, determining the probability of reinfection by making a large-scale testing of persons already found positive several months ago would strongly help to get a better visibility of the future outbreak trajectory.