In the context of few available modeling data on COVID-19 epidemic in France, the purpose of our study was to provide a one-month forecast of the spreading dynamic of the virus across all metropolitan French Regions, and to assess hospitals burden, especially regarding ICU beds and ventilation needs.

We modeled the propagation of COVID-19 from March 10 to April 14, across all metropolitan French Regions. At the national level, the total number of infected cases is expected to range from 22,872 in the best case (R₀ = 1.5) to 161,832 in the worst considered case (R₀ = 3). Regarding the total number of deaths, it is expected to vary from 1,021 to 11,032, respectively. At the regional level, all ICU capacities may be overrun in the worst scenario, Centre-Val de Loire being the last region to reach its limits on April 12. Only seven Regions may lack ICU beds in the mid scenario (R₀ = 2.25) and only one in the best case. In the three scenarios, Corse may be the first Region to see its ICU capacities overrun with a delay of one week between each scenario, which may be due to its low ICU capacity (18 beds). The two other Regions, whose capacity will be overrun shortly after, are Grand-Est and Bourgogne-Franche-Comté, despite their high number of ICU beds (465 and 198, respectively).

COVID-19 mortality risk is not only dependent on the intrinsic virus’ characteristics, but depends also on health care capacities, especially ICU. Italy is already seeing its ICU capacities exceeded, as well as several hospitals in France. However, few studies have tried to forecast ICU needs. Grasselli and colleagues used linear and exponential models to estimate ICU demand in Lombardy, Italy, from March 7 to March 20²⁸. They concluded that the health care system could not sustain an uncontrolled outbreak, and that strong containment measures were needed. Remuzzi and Remuzzi fitted exponential models and predicted that the Italian health care system could be at maximum capacity by March 14²⁹. Here, we found that ICU capacities would be rapidly exceeded in several Regions in France, even in optimistic scenarios. Incapacity to provide adequate treatment to critically ill patients could further increase the already substantial death toll of the epidemic.

Besides limits inherent to each transmission model, this work has several specific limitations. The model was run for each catchment area independently, as we did not model population movements between catchment areas. Although it is theoretically feasible, it seems unnecessary in this context. Infected cases are already present in most locations, meaning transmission is likely to be mainly driven locally, not by inter-areas transfers. Moreover, control measures are already implemented to limit population movements. We are only presenting forecasts at one month, as long term predictions may be unreliable due to the few data available to calibrate the model concerning the epidemic in France. The critical factor that remains unknown to this date is the potential impact of seasonality on the transmission dynamic of COVID-19. Danon and colleagues modeled seasonal transmission by introducing a time-varying transmission rate.²¹ They estimated that a 50% reduction in transmission during summer months would result in a smaller epidemic before the summer, followed by a resurgence in cases in the following winter. However, whether SARS-CoV-2 transmission will be affected by seasonal variations remains unclear. Although many infectious diseases have seasonal patterns, like influenza or other coronaviruses, newly introduced viruses can behave differently. Several experts suggest that the impact of seasonality on COVID-19 transmission might be very modest,^30,31 therefore we did not included such a seasonality in our model at the time. Also, we decided to explore only R₀ values between 1.5 and 3, as it seems to be the most reliable estimates at the moment, according to Abbott and colleagues²⁰. Finally, we did not make a distinction between symptomatic and asymptomatic cases, whereas some modelers decided to create two compartments (infectious asymptomatic and infectious symptomatic). We believed it was unnecessary in this context as we are not focusing on detection or control measures, and it should not impact the interpretation of our results.

Regarding the prediction of ICU needs, the ICU capacities used in this study are theoretical and based on annual data,²⁴ and may not reflect exactly current ICU capacities. However, the potential discrepancies are likely to be modest and should not impact the interpretation of the results. More importantly, we assumed that ICU capacities could entirely be dedicated to COVID-19 critical patients. In France, ICU wards tend to have more than 80% occupancy rate (personal communication with clinicians), hence our analysis already assumes an important patient care reorganization, almost doubling current capacities. Also, we assumed a fixed length of stay of 15 days in ICU as observed in foreign countries. This value could vary across patients and locations, and could slightly bias the estimation of ICU needs in our study. To overcome this bias, we plan to use hospitalization data provided by regional health agencies (ARS), which may help to have better predictions of beds use.

We restricted our model to metropolitan France, as overseas Regions are at a lower epidemic stage at the moment, and the transmission dynamics are likely to differ from metropolitan France. Finally, it must be noted that spatial division of the French territory used in this model does not exactly reflect administrative boundaries of the French Regions, as it was based on the merge of each Voronoi polygons representing the catchment areas of referral centers. However, division by catchment areas might help to better estimate the pressure on the referral centers, as people are more likely to be referred to hospitals based on geographical distance rather than administrative boundaries.

To mitigate the epidemic, the French government announced a series of nation-wide measures, of increasing importance. On February 29, gatherings were restricted to 5,000 persons in confined settings. This threshold has since been revised downwards, with 5,000 persons on March 8, and 100 persons on March 13. On March 12, schools and universities were asked to close starting from March 16, and voluntary household quarantine and social distancing of those over 70 years of age were recommended. Finally, on March 14, the stage 3 of the epidemic was declared. Consequently, all non-essential public places (i.e. non-food shops, restaurants, pubs,…) are closed, and people are enjoined to stay home, limit social interactions, and travels as much as possible. These mitigation measures were not directly implemented in the present study, but their impact was assessed indirectly by modifying the value of the reproduction number.