|Figure 1: Progression in France from daily hospital data from French government public database. The points are the daily hospital data (hospitalizations in purple, intensive care units (réanimations) in red, deaths in black). The curves are my best-fit models on regional hospital data (ran on 4 May 2020, see my article). These models assume that in each French region, the R factor (average number of people contaminated per single infectious person) was constant before the lockdown and another constant between the lockdown of 17 March 2020 and the date of 21 June 2020 (the national lockdown ended on 11 May 2020). After 21 June 2020, the models assume that all regions share the same constant R value as follows: 21 June to 30 October 2020 (no lockdown): R=1.23; 30 October to 21 December 2020 (2nd lockdown): R=0.7, 0.85, or 1 (hence the 3 curves); 21 to 28 December 2020 (Christmas lift of lockdown): R=1.7; After 28 December 2020 (resumed lockdown): R takes same value as in 2nd lockdown. The curves beyond 4 May 2020 are extrapolations from the fits to the hospital data up to that day. I only allowed myself to choose the pivot date of 21 June 2020 to fit the transition from end of the 1st wave to onset of the 2nd wave up to 30 October 2020. The vertical axis is logarithmic: each vertical step represents a multiplication by 10 (the horizontal lines are for daily values of 1, 10, 100, and 1000). Exponential rises and decreases appear linear in such a plot. The weekly drops and rises are caused by under-reporting on weekends and over-reporting on Mondays.|
|Figure 3: Mean death rates per country per super-wave, which each begin on August 1st and end on July 31st of the following year. These time periods are tailored for countries in the Northern hemisphere. Left: 2nd superwave vs 1st superwave. right: 3rd (ongoing) superwave vs previous two superwaves. The arrows highlight the current death rate (with 7-day smoothing), instead of the mean. The upwards arrows indicate worsening, while the downwards ones indicate improvement. The colors of the countries follow their flags in these first two charts. Data from Our World in Data.|
|Figure 4: Effects of COVID-19 vaccination in selected countries: a) Global protection vs. time. Top left: Current death rate per fraction of doubly vaccinated. The colors of all countries now follow continents. Top right: Simple model for vacine protection over time. Based on model by S. Tartof et al., Effectiveness of mRNA BNT162b2 COVID-19 vaccine up to 6 months in a large integrated health system in the USA: a retrospective cohort study, The Lancet 398, 1407, Oct. 16 2021, 2nd row: Estimated vaccine protection (from the convolution of the previous rates of 2nd and 3rd doses by the estimated vaccine efficiency of the top right panel) [left] and decrease in R factor thanks to vaccine protection (right). This corresponds to (1-[vaccine protection])2. Data from Our World in Data.|
|Figure 5: Effects of the different variants. Left: Weekly evolution of Delta and Omicron variants in selected European Union countries. The numbers of cases per variant are extrapolated from sequencing analyses performed on a small fraction of cases. The statistical uncertainties are nevertheless too small to see (but the sequenced samples may be biased). Data from the European Centre for Disease Prevention and Control (ECDC), using the GISAID EpiCov and The European Surveillance System (TESSy) databases, updated weekly. Right: Case-fatality rate in selected countries: The daily rates of cases are divided by the daily rates of deaths, where the cases are shifted to 15 days earlier. Data from Our World in Data. The strong decreases during December in most selected countries are very probably linked to the rise of the less dangerous Omicron variant.|
|Figure 6: Effects of COVID-19 vaccination in France: b) COVID-19 rates per vaccination history Rates of COVID-19 hospitalizations (top left), arrivals in critical care (top right), and hospital deaths (bottom) per vaccination history in France. Only the dominant vaccination history classes are shown. 0 stands for un-vaccinated. 3 is limited to those who received their booster shots more than 6 months after their 2nd shots. Data from Direction de la Recherche, des Études, de l'Évaluation et des Statistiques (DREES), updated weekly.|
|Figure 7: Effects of COVID-19 vaccination in France: c) COVID-19 daily hospitalization rates per vaccination history for different age groups. Only shown are daily rates based on 3 or more hospitalizations (i.e. relative accuracy better than 40%). Only the dominant vaccination history classes are shown. 0 stands for un-vaccinated. 3 is limited to those who received their booster shots more than 6 months after their 2nd shots. Data from Direction de la Recherche, des Études, de l'Évaluation et des Statistiques (DREES), updated weekly.|
|Figure 8: Effects of COVID-19 vaccination in France: d) COVID-19 daily hospital death rates per vaccination history for different age groups. Only shown are daily rates based on 3 or more deaths (i.e. relative accuracy better than 40%). Thus, the evolutions of death rates for 0-19 and 20-39 year olds are not shown, for lack of accurate data. Only the dominant vaccination history classes are shown. 0 stands for un-vaccinated. 3 is limited to those who received their booster shots more than 6 months after their 2nd shots. Data from Direction de la Recherche, des Études, de l'Évaluation et des Statistiques (DREES), updated weekly.|
|Figure 9: Effects of COVID-19 vaccination in France: e) Boost of protection from vaccinations per vaccination history and age: Vaccine boost against hospitalizations (left), critical care (middle) and deaths in hospitals (right) by age and vaccination history, averaged over time. A number of 10 indicates that a person of that vaccination history and age has 10 times less chances of being affected (hospitalized, sent to critical care or dying in a hospital, according to the chart) compared to non-vaccinated people of the same age. Numbers in parentheses have uncertainties greater than a factor 2 by less than a factor 4. Missing numbers have uncertainties greater than a factor 4. Colors go from dark blue (high positive protection) to dark red (high negative protection). The numbers are from maximum likelihood fits assuming Poisson distributions for the cases (hospitalizations, critical care arrivals or deaths) of the target vaccination status, weighted by the square root of the sum of the daily cases for the target and non-vaccinated statuses. Only the dominant vaccination history classes are shown. 0 stands for un-vaccinated. 3 is limited to those who received their booster shots more than 6 months after their 2nd shots. Data from Direction de la Recherche, des Études, de l'Évaluation et des Statistiques (DREES), updated weekly.|
Analysis (22 February 2022):
Analysis (20 January 2022):
Analysis (12 January 2022):
Analysis (9 January 2022):
Analysis (5 January 2022):
Analysis (27 December 2021):
Analysis (17 December 2021):
I now added estimates of the protection against hospitalization and deaths by vaccination history and age in the bottom plots of Figure 4 (now 9). The boost from recent vaccinations against hospitalization in France is above 10 and typically 15, at a given age. This higher boost relative to the previous estimate without considering age compensates the fact that those who got their first shots were the elderly, who are more fragile.
Analysis (15 December 2021):
I added 3 charts showing the daily evolution of hospital arrivals, critical care arrivals and hospital deaths, all for COVID-19, now split by the vaccination history.
These new plots indicate that:
Analysis (23 November 2021):
I added three new charts that study the impact of vaccinations on the effective reproduction number, also called R, which measures the average number of persons contaminated by a single infectious person.
Analysis (11 November 2021):
Analysis (23 October 2021):
Analysis (3 October 2021):
Analysis (20 December 2020):
Analysis (20 November 2020):
Analysis (15 November 2020):
Analysis (29 October 2020):
Analysis (made on 30 September 2020):
Article: G. A. Mamon 2020,
Regional analysis of COVID-19 in France from fit of hospital data with
different evolutionary models
(13 May 2020, version 4: 17
Abstract (Résumé en français):
The SIR evolutionary model predicts too sharp a decrease of the fractions of people infected with COVID-19 in France after the start of the national lockdown, compared to what is observed. I fit the daily hospital data: arrivals in regular and critical care units, releases and deaths, using extended SEIR models. These involve ratios of evolutionary timescales to branching fractions, assumed uniform throughout a country, and the basic reproduction number, R0, before and during the national lockdown, for each region of France. The joint-region Bayesian analysis allows precise evaluations of the time/fraction ratios and pre-hospitalized fractions. The hospital data are well fit by the models, except the arrivals in critical care, which decrease faster than predicted, indicating better treatment over time. Averaged over France, the analysis yields R0 = 3.4±0.1 before the lockdown and 0.65±0.04 (90% c.l.) during the lockdown, with small regional variations. On 11 May 2020, the Infection Fatality Rate in France was 4 ± 1% (90% c.l.), while the Feverish vastly outnumber the Asymptomatic, contrary to the early phases. Without the lockdown nor social distancing, over 2 million deaths from COVID-19 would have occurred throughout France, while a lockdown that would have been enforced 10 days earlier would have led to less than 1000 deaths. The fraction of immunized people reached a plateau below 1% throughout France (3% in Paris) by late April 2020 (95% c.l.), suggesting a lack of herd immunity. The widespread availability of face masks on 11 May, when the lockdown was partially lifted, should keep R0 below unity if at least 46% of the population wear them outside their home. Otherwise, without enhanced other social distancing, a second wave is inevitable and cause the number of deaths to triple between early May and October (if R0 = 1.2) or even late June (if R0 = 2).
Press release: Une nouvelle analyse régionale du COVID-19 en France
Presentation: Analysis of French COVID-19 hospital data with a SEAFHCDRO model (5 May 2020, Institut d'Astrophysique de Paris)
My thoughts on the spread of the pandemic A few things to know about the spread of COVID-19 (revised version of 2 April 2020)
Article in The Conversation (1 April 2020, in French, by André Klarsfeld, with charts from myself) Pour comprendre la pandémie, les courbes valent mieux que les avalanches de chiffres. Reproduced in weekly magazine La Tribune and monthly Santé Magazine.