Using Early Data to Estimate the Actual Infection Fatality Ratio from COVID-19 in France

Abstract

The number of screening tests carried out in France and the methodology used to target the patients tested do not allow for a direct computation of the actual number of cases and the infection fatality ratio (IFR). The main objective of this work is to estimate the actual number of people infected with COVID-19 and to deduce the IFR during the observation window in France. We develop a `mechanistic-statistical' approach coupling a SIR epidemiological model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. The actual number of infected cases in France is probably higher than the observations: we find here a factor ×8 (95%-CI: 5-12) which leads to an IFR in France of 0.5% (95%-CI: 0.3-0.8) based on hospital death counting data. Adjusting for the number of deaths in nursing homes, we obtain an IFR of 0.8% (95%-CI: 0.45-1.25). This IFR is consistent with previous findings in China (0.66%) and in the UK (0.9%) and lower than the value previously computed on the Diamond Princess cruse ship data (1.3%).

Keywords: Bayesian inference; COVID-19; SIR model; case fatality rate; infection fatality ratio; mechanistic-statistical model.

Figure A1

Joint posterior distributions of $(\alpha ,\kappa )$, $(t_0,\alpha )$ and $(t_0,\kappa )$.

Figure A1

Joint posterior distributions of $(\alpha ,\kappa )$, $(t_0,\alpha )$ and $(t_0,\kappa )$.

Figure A2

Joint posterior distributions of $(\alpha ,\kappa )$, $(t_0,\alpha )$ and $(t_0,\kappa )$ obtained with a more informative prior.

Figure A3

Dynamics of the IFR in France. Solid line: average value obtained from the posterior distribution of the parameters. Dotted curves: 0.025 and 0.975 pointwise quantiles.

Figure A4

Posterior distribution of the basic reproduction number $R_0$ in France.

Figure 1

Expected number of observed cases associated with the MLE vs. number of cases actually detected (total cases). The curve corresponds to cumulated values of the expected observation $n_t{p}_t^{\ast }$ given by the model, and the crosses correspond to the data (cumulated values of ${\widehat{\delta }}_t$).

Figure 2

Distribution of the cumulated number of infected cases ($I\left(t\right)+R\left(t\right)$) across time. Solid line: average value obtained from the posterior distribution of the parameters. Dotted curves: 0.025 and 0.975 pointwise posterior quantiles. Blue crosses: data (cumulated values of ${\widehat{\delta }}_t$).