An international team of researchers has found that just 4.4 percent of people in France have been infected with the SARS-CoV-2 virus


An international team of researchers has found that just 4.4 percent of people in France have been infected with the SARS-CoV-2 virus – a percentage far below that needed for herd immunity.

In their paper published in the journal Science, the group describes their study of hospital and surveillance data and what it showed.

As the global pandemic continues to spread around the globe, many nations have begun to grapple with the issue of when to ease lockdown restrictions put it place to slow the spread of COVID-19.

Such restrictions were enacted to “flatten the curve” to prevent hospitals and other healthcare facilities from being overrun. But such restrictions have led to economic problems – business closings, layoffs and slowing of sales – which have sent many countries into recession.

And as medical scientists have warned that a vaccine or even an effective treatment for the disease may be a year or more in the future, world leaders have come under pressure to lift restrictions now – and many have relented.

On May 11, many of the restrictions in France were lifted, allowing people to return to work, albeit with new rules in place, such as social distancing.

As countries including France have begun lifting restrictions, medical scientists have begun to speak out about the problems that could result if the restrictions are lifted too quickly.

They note that in the absence of a vaccine, the only way out of the pandemic is through herd immunity, in which enough people carry antibodies that the virus burns itself out (assuming those with the antibodies truly are immune).

Most scientists agree that herd immunity occurs when approximately 65 to 75% of a population has been infected. In this new effort, the researchers have found that France is still very far away from herd immunity, and therefore faces a likely second wave of infections as restrictions are eased.

The work by the team involved analyzing COVID-19 related hospital records, surveillance data from hospitals, and data from the cruise ship Diamond Princess.

The analysis showed that just 3.6 percent of those infected with the SARS-CoV-2 virus required hospitalization, and just 0.7 of such patients died. They also found the lockdown reduced the transmission rate by 78%, and that just 4.4 percent of the country’s population has been infected—very far below the threshold for herd immunity.

As of 7 May 2020, there were 95,210 incident hospitalizations due to SARS-CoV-2 reported in France and 16,386 deaths in hospitals, with the east of the country and the capital, Paris, particularly affected (Fig. 1, A and B).

The mean age of hospitalized patients was 68ya and the mean age of the deceased was 79ya with 50.0% of hospitalizations occurring in individuals >70ya and 81.6% of deaths within that age bracket; 56.2% of hospitalizations and 60.3% of deaths were male (Fig. 1, C to E).

To reconstruct the dynamics of all infections, including mild ones, we jointly analyze French hospital data with the results of a detailed outbreak investigation aboard the Diamond Princess cruise ship where all passengers were subsequently tested (719 infections, 14 deaths currently).

By coupling the passive surveillance data from French hospitals with the active surveillance performed aboard the Diamond Princess, we disentangle the risk of being hospitalized in those infected from the underlying probability of infection (5, 6).

Fig. 1 COVID-19 hospitalizations and deaths in France.
(A) Cumulative number of general ward and ICU hospitalizations, ICU admissions and deaths from SARS-CoV-2 in France. The green line indicates the time when the lockdown was put in place in France. (B) Distribution of deaths in France. Number of (C) hospitalizations, (D) ICU and (E) deaths by age group and sex in France.

We find that 3.6% of infected individuals are hospitalized (95% CrI: 2.1–5.6), ranging from 0.2% (95% CrI: 0.1–0.2) in females under <20ya to 45.9% (95% CrI: 27.2–70.9) in males >80ya (Fig. 2A and table S1).

Once hospitalized, on average 19.0% (95% CrI: 18.7–19.4%) patients enter ICU after a mean delay of 1.5 days (fig. S1). We observe an increasing probability of entering ICU with age—however, this drops for those >70ya (Fig. 2B and table S2).

Overall, 18.1% (95% CrI: 17.8–18.4) of hospitalized individuals go on to die (Fig. 2C). The overall probability of death among those infected (the Infection Fatality Ratio, IFR) is 0.7% (95% CrI: 0.4–1.0), ranging from 0.001% in those under 20ya to 10.1% (95% CrI: 6.0–15.6) in those >80ya (Fig. 2D and table S2).

Our estimate of overall IFR is similar to other recent studies that found values of between 0.5 and 0.7% for the Chinese epidemic (6–8). We find men have a consistently higher risk than women of hospitalization (RR 1.25, 95% CrI: 1.22–1.29), ICU admission once hospitalized (RR: 1.61, 95% CrI: 1.56–1.67) and death following hospitalization (RR: 1.47, 95% CrI: 1.42–1.53) (fig. S2).

Fig. 2 Probabilities of hospitalization, ICU admittance and death.
(A) Probability of hospitalization among those infected as a function of age and sex. (B) Probability of ICU admission among those hospitalized as a function of age and sex. (C) Probability of death among those hospitalized as a function of age and sex. (D) Probability of death among those infected as a function of age and sex. For each panel, the black line and grey shaded region represents the overall mean across all ages. The boxplots represent the 2.5, 25, 50, 75 and 97.5 percentiles of the posterior distributions.

We identify two clear subpopulations in those cases that are hospitalized: individuals that die quickly upon hospital admission (15% of fatal cases, mean time to death of 0.67 days) and individuals who die after longer time periods (85% of fatal cases, mean time to death of 13.2 days) (fig. S3).

The proportion of fatal cases who die rapidly remains approximately constant across age-groups (fig. S4 and table S3). Potential explanations for different subgroups of fatal cases include heterogeneous patterns of healthcare seeking, access to care, underlying comorbidities, such as metabolic disease and other inflammatory conditions. A role for immunopathogenesis has also been proposed (9–12).

We next fit national and regional transmission models to ICU admission, hospital admission, and bed occupancy (both ICU and general wards) (Fig. 3, A to D, fig. S5, and tables S4 to S6), allowing for reduced age-specific daily contact patterns following the lockdown and changing patterns of ICU admission over time (fig. S17).

We find that the basic reproductive number R0 prior to the implementation of the lockdown was 2.90 (95% CrI: 2.80–2.99). The lockdown resulted in a 77% (95% CI: 76–78) reduction in transmission, with the reproduction number R dropping to 0.67 (95% CrI: 0.65–0.68). We forecast that by the 11 May 2020, 2.8 million (range: 1.8–4.7, when accounting for uncertainty in the probability of hospitalization given infection) people will have been infected, representing 4.4% (range: 2.8–7.2) of the French population (Fig. 3E). This proportion will be 9.9% (range: 6.6–15.7) in Ile-de-France, which includes Paris, and 9.1% (range: 6.0–14.6) in Grand Est, the two most affected regions of the country (Fig. 3F and fig. S5).

Assuming a basic reproductive number of R0 = 3.0, it would require around 65% of the population to be immune for the epidemic to be controlled by immunity alone. Our results therefore strongly suggest that, without a vaccine, herd immunity on its own will be insufficient to avoid a second wave at the end of the lockdown. Efficient control measures need to be maintained beyond the 11 May.

Fig. 3 Time course of the SARS-CoV-2 epidemic to 11 May 2020.
(A) Daily admissions in ICU in metropolitan France. (B) Number of ICU beds occupied in metropolitan France. (C) Daily hospital admissions in metropolitan France. (D) Number of general ward beds occupied in metropolitan France (E) Daily new infections in metropolitan France (logarithmic scale). (F) Predicted proportion of the population infected by 11 May 2020 for each of the 13 regions in metropolitan France. (G) Predicted proportion of the population infected in metropolitan France. The black circles in panels (A), (B), (C) and (D) represent hospitalization data used for the calibration and the open circles hospitalization data that were not used for calibration. The dotted lines in panels (E) and (G) represent the 95% uncertainty range stemming from the uncertainty in the probability of hospitalization following infection.

Our model can help inform the ongoing and future response to COVID-19. National ICU daily admissions have gone from 700 at the end of March to 66 on 7 May.

Hospital admissions have declined from 3600 to 357 over the same time period, with consistent declines observed throughout France (fig. S5). By 11 May we project 3900 (range: 2600–6300) daily infections across the country, down from between 150,000–390,000 immediately prior to the lockdown.

At a regional level, we estimate that 58% of infections will be in Ile-de-France and Grand Est combined. We find that the time people spend in ICU appears to differ across the country, which may be due to differences in health care practices (table S5).

Using our modeling framework, we are able to reproduce the observed number of hospitalizations by age and sex in France and the number of observed deaths aboard the Diamond Princess (fig. S6).

As a validation, our approach is also able to correctly identify parameters in simulated datasets where the true values are known (fig. S7). As cruise ship passengers may represent a different, healthier population than average French citizens, we run a sensitivity analysis where Diamond Princess passengers are 25% less likely to die than French citizens (Fig. 4 and fig. S8).

We also run sensitivity analyses with longer delays between symptom onset and hospital admission, missed infections aboard the Diamond Princess, equal attack rates across all ages, reduced infectivity in younger individuals, a contact matrix with unchanged structure before/during the lockdown and one with very high isolation of elderly individuals during the lockdown.

These different scenarios result in mean IFRs from 0.5 to 0.9%, the proportion of the population infected by the 11 May 2020 ranging from 1.7–8.9%, the number of daily infections at this date ranging from 1700 to 9600 and a range of reproductive numbers post lockdown of 0.62–0.73 (Fig. 4, figs. S8 to S15, and tables S7 to S12).

Fig. 4 Sensitivity analyses considering different modeling assumptions.
(A) Infection fatality rate (%). (B) Estimated reproduction numbers before (R0) and during lockdown (Rlockdown). (C) Predicted daily new infections on 11 May. (D) Predicted proportion of the population infected by 11 May. The different scenarios correspond to: Children less inf. – Individuals <20ya are half as infectious as adults; No Change CM – the structure of the contact matrix is not modified by the lockdown; CM SDE – Contact matrix after lockdown with very high social distancing of the elderly; Constant AR – Attack rates are constant across age groups; Higher IFR – French people 25% more likely to die than Diamond Princess passengers; Higher AR DP – 25% of the infections were undetected on the Diamond Princess cruise ship; Delay Distrib – Single hospitalization to death delay distribution; Higher delay to hosp – 8 days on average between symptoms onset and hospitalization for patients who will require an ICU admission and 9 days on average between symptoms onset and hospitalization for the patients who will not. For estimates of IFR and reproduction numbers before and during lockdown, we report 95% credible intervals. For estimates of daily new infections and proportion of the population infected by 11 May, we report the 95% uncertainty range stemming from the uncertainty in the probability of hospitalization given infection.

A seroprevalence of 3% (range: 0–3%) has been estimated among blood donors in Hauts-de-France, which is consistent with our model predictions (range: 1–3%) for this population if we account for a 10-day delay for seroconversion (13, 14). Future additional serological data will help further refine estimates of the proportion of the population infected.

While we focus on deaths occurring in hospitals, there are also non-hospitalized COVID-19 deaths, including >9000 in retirement homes in France (15). We explicitly removed retirement home population from our analyses as transmission dynamics may be different in these closed populations.

This means our estimates of immunity in the general population are unaffected by deaths in retirement homes, however, in the event of large numbers of non-hospitalized deaths in the wider community, we would underestimate the proportion of the population infected. Analyses of excess death will be important to explore these issues.

This study shows the massive impact the French lockdown had on SARS-CoV-2 transmission. Our modeling approach has allowed us to estimate underlying probabilities of infection, hospitalization and death, which is essential for the interpretation of COVID-19 surveillance data.

The forecasts we provide can inform lockdown exit strategies. Our estimates of a low level of immunity against SARS-CoV-2 indicates that efficient control measures that limit transmission risk will have to be maintained beyond the 11 May 2020 to avoid a rebound of the epidemic.

More information: Henrik Salje et al. Estimating the burden of SARS-CoV-2 in France, Science (2020). DOI: 10.1126/science.abc3517

References and Notes

  1. M. U. G. Kraemer, C.-H. Yang, B. Gutierrez, C.-H. Wu, B. Klein, D. M. Pigott, L. du essis, N. R. Faria, R. Li, W. P. Hanage, J. S. Brownstein, M. Layan, A. Vespignani, H. Tian, C. Dye, O. G. Pybus, S. V. Scarpino; Open COVID-19 Data Working Group, The effect of human mobility and control measures on the COVID-19 epidemic in China. Science 368, 493–497 (2020). doi:10.1126/science.abb4218pmid:32213647Abstract/FREE Full TextGoogle Scholar
  2. H. Tian, Y. Liu, Y. Li, C.-H. Wu, B. Chen, M. U. G. Kraemer, B. Li, J. Cai, B. Xu, Q. Yang, B. Wang, P. Yang, Y. Cui, Y. Song, P. Zheng,Q. Wang, O. N. Bjornstad, R. Yang, B. T. Grenfell, O. G. Pybus, C. Dye, An investigation of transmission control measures during the first 50 days of the COVID-19 epidemic in China. Science 368, 638–642 (2020). doi:10.1126/science.abb6105pmid:32234804Abstract/FREE Full TextGoogle Scholar
  3. J. Lourenço, R. Paton, M. Ghafari, M. Kraemer, C. Thompson, P. Simmonds, P. Klenerman, S. Gupta, Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-CoV-2 epidemic. medRxiv 2020.03.24.20042291 [Preprint]. 26 March 2020.
  4. L. Bao, W. Deng, H. Gao, C. Xiao, J. Liu, J. Xue, Q. Lv, J. Liu, P. Yu, Y. Xu, F. Qi, Y. Qu, F. Li, Z. Xiang, H. Yu, S. Gong, M. Liu, G. Wang, S. Wang, Z. Song, W. Zhao, Y. Han, L. Zhao, X. Liu, Q. Wei, C. Qin, Reinfection could not occur in SARS-CoV-2 infected rhesus macaques. bioRxiv 2020.03.13.990226 [Preprint]. 14 March 2020.
  5. J. Lessler, H. Salje, M. D. Van Kerkhove, N. M. Ferguson, S. Cauchemez, I. Rodriquez-Barraquer, R. Hakeem, T. Jombart, R. Aguas, A. Al-Barrak, D. A. T. Cummings; MERS-CoV Scenario and Modeling Working Group, Estimating the severity and subclinical burden of Middle East respiratory syndrome coronavirus infection in the Kingdom of Saudi Arabia. Am. J. Epidemiol. 183, 657–663 (2016). doi:10.1093/aje/kwv452pmid:26851269CrossRefPubMedGoogle Scholar
  6. R. Verity, L. C. Okell, I. Dorigatti, P. Winskill, C. Whittaker, N. Imai, G. Cuomo-nnenburg, H. Thompson, P. G. T. Walker, H. Fu, A. Dighe, J. T. Griffin, M. Baguelin, S. Bhatia, A. Boonyasiri, A. Cori, Z. Cucunubá, R. FitzJohn, K.aythorpe, W. Green, A. Hamlet, W. Hinsley, D. Laydon, G. Nedjati-Gilani, S. Riley, S. van Elsland, E. Volz, H. Wang, Y. Wang, X. Xi, C. A. Donnelly, A. C. Ghani, N. M. Ferguson, Estimates of the severity of coronavirus disease 2019: A model-based analysis. Lancet Infect. Dis. 10.1016/S1473-3099(20)30243-7 (2020). doi:10.1016/S1473-3099(20)30243-7pmid:32240634CrossRefPubMedGoogle Scholar
  7. T. W. Russell, J. Hellewell, C. I. Jarvis, K. van Zandvoort, S. Abbott, R. Ratnayake, S. Flasche, R. M. Eggo, W. J. Edmunds, A. J. Kucharski; Cmmid Covid-Working Group, Estimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020. Euro Surveill. 25, 2000256 (2020). doi:10.2807/1560-7917.ES.2020.25.12.2000256pmid:32234121CrossRefPubMedGoogle Scholar
  8. K. Mizumoto, K. Kagaya, G. Chowell, Early epidemiological assessment of the transmission potential and virulence of coronavirus disease 2019 (COVID-19) in Wuhan City: China, January-February, 2020. medRxiv 2020.02.12.20022434 [Preprint]. 13 March 2020.
  9. L. Peeples, News Feature: Avoiding pitfalls in the pursuit of a COVID-19 vaccine. Proc. Natl. Acad. Sci. U.S.A. 117, 8218–8221 (2020). doi:10.1073/pnas.2005456117pmid:32229574FREE Full TextGoogle Scholar
  10. D. Ricke, R. W. Malone, Medical Countermeasures Analysis of 2019-nCoV and Vaccine Risks for Antibody-Dependent Enhancement (ADE), 27 February 2020;
  11. J. Yang, Y. Zheng, X. Gou, K. Pu, Z. Chen, Q. Guo, R. Ji, H. Wang, Y. Wang, Y. Zhou, Prevalence of comorbidities and its effects in patients infected with SARS-CoV-2: A systematic review and meta-analysis. Int. J. Infect. Dis. 94, 91–95 (2020). doi:10.1016/j.ijid.2020.03.017pmid:32173574CrossRefPubMedGoogle Scholar
  12. M. Bolles, D. Deming, K. Long, S. Agnihothram, A. Whitmore, M. Ferris, W. Funkhouser, L. Gralinski, A. Totura, M. Heise, R. S. Baric, A double-inactivated severe acute respiratory syndrome coronavirus vaccine provides incomplete protection in mice and induces increased eosinophilic proinflammatory pulmonary response upon challenge. J. Virol. 85, 12201–12215 (2011). doi:10.1128/JVI.06048-11pmid:21937658Abstract/FREE Full TextGoogle Scholar
  13. A. Fontanet, L. Tondeur, Y. Madec, R. Grant, C. Besombes, N. Jolly, S. F. Pellerin, M.-N. Ungeheuer, I. Cailleau, L. Kuhmel, S. Temmam, C. Huon, K.-Y. Chen, B. Crescenzo, S. Munier, C. Demeret, L. Grzelak, I. Staropoli, T. Bruel, P. Gallian, S. Cauchemez, S. van der Werf, O. Schwartz, M. Eloit, B. Hoen, Cluster of COVID-19 in northern France: A retrospective closed cohort study. medRxiv 2020.04.18.20071134 [Preprint]. 23 April 2020.
  14. L. Grzelak, S. Temmam, C. Planchais, C. Demeret, C. Huon, F. Guivel, I. Staropoli, M. Chazal, J. Dufloo, D. Planas, J. Buchrieser, M. M. Rajah, R. Robinot, F. Porrot, M. Albert, K.-Y. Chen, B. Crescenzo, F. Donati, F. Anna, P. Souque, M. Gransagne, J. Bellalou, M. Nowakowski, M. Backovic, L. Bouadma, L. Le Fevre, Q. Le Hingrat, D. Descamps, A. Pourbaix, Y. Yazdanpanah, L. Tondeur, C. Besombes, M.-N. Ungeheuer, G. Mellon, P. Morel, S. Rolland, F. Rey, S. Behillil, V. Enouf, A. Lemaitre, M.-A. Creach, S. Petres, N. Escriou, P. Charneau, A. Fontanet, B. Hoen, T. Bruel, M. Eloit, H. Mouquet, O. Schwartz, S. van der Werf, SARS-CoV-2 serological analysis of COVID-19 hospitalized patients, pauci-symptomatic individuals and blood donors. medRxiv 2020.04.21.20068858 [Preprint]. 24 April 2020.
  15. French Government website, Info Coronavirus Covid 19 (in French);
  16. H. Salje, C. Tran Kiem, Code and data for: Estimating the burden of SARS-CoV-2 in France, Version 1.0, Zenodo (2020);
  17. Field Briefing: Diamond Princess COVID-19 Cases, 20 Feb Update (2020);
  18. Ministry of Health, Labour and Welfare, About new coronavirus infection (in Japanese);
  19. H. Nishiura, D. Klinkenberg, M. Roberts, J. A. P. Heesterbeek, Early epidemiological assessment of the virulence of emerging infectious diseases: A case study of an influenza pandemic. PLOS ONE 4, e6852 (2009). doi:10.1371/journal.pone.0006852pmid:19718434CrossRefPubMedGoogle Scholar
  20. G. Béraud, S. Kazmercziak, P. Beutels, D. Levy-Bruhl, X. Lenne, N. Mielcarek, Y. Yazdanpanah, P.-Y. Boëlle, N. Hens, B. Dervaux, The French connection: The first large population-based contact survey in France relevant for the spread of infectious diseases. PLOS ONE 10, e0133203 (2015). doi:10.1371/journal.pone.0133203pmid:26176549CrossRefPubMedGoogle Scholar
  21. K. Mizumoto, K. Kagaya, A. Zarebski, G. Chowell, Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Euro Surveill. 25, (2020). doi:10.2807/1560-7917.ES.2020.25.10.2000180pmid:32183930CrossRefPubMedGoogle Scholar
  22. Stan Development Team, RStan: the R interface to Stan (2020);
  23. Z. Du, X. Xu, Y. Wu, L. Wang, B. J. Cowling, L. A. Meyers, Serial interval of COVID-19 among publicly reported confirmed cases. Emerg. Infect. Dis. 10.3201/eid2606.200357 (2020). doi:10.3201/eid2606.200357pmid:32191173CrossRefPubMedGoogle Scholar
  24. Q. Bi, Y. Wu, S. Mei, C. Ye, X. Zou, Z. Zhang, X. Liu, L. Wei, S. A. Truelove, T. Zhang, W. Gao, C. Cheng, X. Tang, X. Wu, Y. Wu, B. Sun, S. Huang, Y. Sun, J. Zhang, T. Ma, J. Lessler, T. Feng, Epidemiology and Transmission of COVID-19 in Shenzhen China: Analysis of 391 cases and 1,286 of their close contacts. medRxiv 2020.03.03.20028423 [Preprint]. 4 March 2020.
  25. L. Tindale, M. Coombe, J. E. Stockdale, E. Garlock, W. Y. V. Lau, M. Saraswat, Y.-H. B. Lee, L. Zhang, D. Chen, J. Wallinga, C. Colijn, Transmission interval estimates suggest pre-symptomatic spread of COVID-19. medRxiv 2020.03.03.20029983 [Preprint]. 6 March 2020. Scholar
  26. S. Funk, socialmixr
  27. O. Diekmann, J. A. Heesterbeek, J. A. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990). doi:10.1007/BF00178324pmid:2117040CrossRefPubMedWeb of ScienceGoogle Scholar
  28. N. Hens, G. M. Ayele, N. Goeyvaerts, M. Aerts, J. Mossong, J. W. Edmunds, P. Beutels, Estimating the impact of school closure on social mixing behaviour and the transmission of close contact infections in eight European countries. BMC Infect. Dis. 9, 187 (2009). doi:10.1186/1471-2334-9-187pmid:19943919CrossRefPubMedGoogle Scholar
  29. Décret n° 2020-260 du 16 mars 2020 portant réglementation des déplacements dans le cadre de la lutte contre la propagation du virus covid-19, Legifrance;
  30. A. Gelman, J. B. Carlin, H. S. Stern, D. B. Rubin, Bayesian Data Analysis (CRC Texts in Statistical Science, Chapman and Hall, ed. 2, 2004).
  31. COVID-19 Community Mobility Report,
  32. J. Wallinga, M. Lipsitch, How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. Biol. Sci. 274, 599–604 (2007). doi:10.1098/rspb.2006.3754pmid:17476782CrossRefPubMedWeb of ScienceGoogle Scholar


Please enter your comment!
Please enter your name here

Questo sito usa Akismet per ridurre lo spam. Scopri come i tuoi dati vengono elaborati.