Gary's blog on the spread of Covid-19 in France and other countries

Updated figures

(analysis after the figures)

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 2: Progression in selected countries for daily cases per million (top), weekly entries in critical care per million (middle), and daily deaths per million (bottom). Data from Our World in Data, whom I thank for the simplicity of embedding into this blog. The countries selected for cases and deaths are France and its major neighbors, as well as countries currently experiencing a high wave (Russia), countries that have experienced strong waves (Hungary and Brazil), countries with a sudden rise from a new variant (South Africa, with Omicron), and the country that vaccinated first (Israel). The countries selected for entries in critical care are the major ones with available data.

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):

Figure 5-left now shows that the Delta variant has decreased, in absolute terms, by a factor 10 in most countries for which I have variant data (even in Germany as I expected on 20 January). Note that the variant data arrives 2-3 weeks late, so in my previous analysis of 20 January, Delta seemed stable, while it had already strongly decreased. This decrease in Delta is good news, as Delta is so much more dangerous than Omicron.
Indeed, one can infer that Omicron is roughly 8 times less deadly than Delta, by glancing at the drop of case fatality rates in all countries surveyed from early January to early February (Figure 5-right).
The protection of triple-vaccinated people against hospitalization and critical care for the 80+ year old people has fallen from a factor of 30 a few weeks ago to 6 or 7 now, as a consequence of their receiving their shots mostly last September, with the vaccine effects wearing off. The French government is currently not recommending (or allowing) 4th shots, and this lack of 4th shots may lead to a rise of arrivals in critical care of this elderly group. Lower age groups, received their 3rd shots more recently, so they are still well protected.

Analysis (20 January 2022):

Figure 5-left shows that while the Omicron variant has overtaken the Delta variant, and is exponentially rising, the Delta variant is in fact roughly constant now. It is therefore not clear that Omicron is growing at the expense of Delta.
While still very high, the boost in protection for the people with 3 doses of vaccine, relative to same age non-vaccinated people, has been decreasing (Figure 9) in comparison with previous weeks.
Omicron has finally surpassed Delta in Germany. My bet is that the case - fatality ratio should decrease fast now, as we see first signs of this in the right panel of Figure 5.
France has reached its lowest case-fatality since the beginning of the pandemic close to 0.1%.

Analysis (12 January 2022):

Figure 2 now contains (middle panel) the evolution of admissions to critical care for COVID-19 symptoms (the cases are now in the top panel and the daily deaths in the bottom one). The critical care arrivals give an indication of hospital saturation.
Thanks to more testing than in the first waves, countries have reached daily cases surpassing all the previous waves.

Analysis (9 January 2022):

Figure 5 now also shows the evolution of variants.
Omicron has overtaken Delta in December 2021, first in Spain and in France, and possibly Germany.
The good news is that the Delta variant is peaking in France, while the less dangerous Omicron variant keeps rising very fast.
But both Omicron and Delta are in exponential growth in Spain.

Analysis (5 January 2022):

A new figure provides the corrected case-fatality rate (CFR), which is the ratio of daily cases over daily fatalities, where the correction is that the cases are shifted to 15 days previous to the deaths. One clearly sees, in all countries but Germany (DEU), a sharp decrease (by a factor of two or more) of the corrected CFR in December, which is very probably caused by the rise of the less dangerous Omicron variant.
If Omicron was negligible on December 1, and is at 50% on January 1 (as appears to be in France), a decrease of the mean corrected CFR by a factor 2 indicates that the corrected Case-Fatality rate of the Omicron variant is 3 times lower than that of the Delta variant.

Analysis (27 December 2021):

By age group, there is clear evidence of the decreasing effects of the vaccine protection with time, as seen by comparing in Figure 6-upper left the rates of hospitalizations for the freshly doubly vaccinated (blue points), those doubly vaccinated between 3 and 6 months ago (green points) and those doubly vaccinated over 6 months ago (red points). This affects all age groups, as also clearly seen in Figure 8. This decrease in vaccine protection with time is in contradiction to the study of Tartof et al. (2021) who found no decrease in vaccine protection against hospitalization in the first 5 months.
By age group, the 3rd (booster) shots (for those who had received their 2nd shot over 6 months ago) have a clear effect compared to those who received their 2nd shot over 6 months ago without a booster shot. This is clear in Figures 6 and 7 (cyan points for those who received their 3rd shot). The people with 3rd shots are 30 times less likely to be hospitalized, be admitted in critical care, or die in a hospital from COVID-19 then unvaccinated people of the same age.
The effects of ages leads to very different conclusions regarding the effects of the vaccinations. While the people who received two vaccinations over 6 months ago (red points) are as likely to be hospitalized and more likely to die in hospitals than unvaccinated people (black points), as seen in Figure 5, once we split according to age group, the doubly-vaccinated over 6 months ago (red points) are roughly 6 times less likely to be hospitalized than the unvaccinated of the same age (black points), as can be seen in Figure 6, and the chart in Figure 8 (left). Similarly, the doubly-vaccinated over 6 months ago are roughly 5 times less likely to die in a hospital from COVID-19 than unvaccinated of the same age (Figure 7 and right panel of Figure 8).
These conclusions are based on data that are dominated by the Delta variant. The arrival of the Omicron variant in late December in France might well lead to a decrease in vaccine protection, given that the Omicron variant is very different from all previous ones. It is encouraging that the rate of COVID-19 cases in South Africa (where Omicron is thought to have started) had been decreasing since mid-December.
The strong protection from renewed vaccinations is at least as strong for severe cases as for hospitalizations (three charts of Figure 8).
The strong protection from renewed vaccinations, normalized by age group, appear to be independent of age group, with the possible exception of the young (0-19 years old). One should note that youth are still rarely vaccinated, and those that are are more likely to present cormobidity risks.
This suggests that the hospital data published by DREES ought to include some measure of cormobidity.

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:

The different vaccination classes follow the same waves.
The recently vaccinated are roughly 8 times less likely to be hospitalized, put in critical care or dying in a hospital, for reasons of COVID-19.
Those having received their two doses over 6 months ago are as likely to be hospitalized than the non-vaccinated, and twice as likely to die in a hospital. This contradicts reports that the protection of the Pfizer/BioNTech vaccine against hospitalization for COVID-19 does not decrease in time, at least for the first 5 months (e.g. Tartof et al. (2021)).
Those receiving booster shots are only 3 times less likely to be hospitalized for COVID-19 than non-vaccinated.
The interpretation of these trends should take into account that the first people vaccinated were the elderly, who are thus the first people to have reached the 6 months after their second dose, while they remain the most fragile.

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.

The first chart (now second panel of Figure 4) is my estimate on the variation of the efficiency of the Pfizer and Moderna vaccines with time, starting on the 2nd injection, E(t).
The second chart (now third panel of Figure 4) displays the effective global protection from vaccines, Q_eff(t) for northern hemisphere countries using the Pfizer and Moderna vaccines. It is the convolution of the effective reproduction number with the daily rates of 2nd and 3rd shots, V₂(t) and V₃(t), respectively. In mathematical terms: Q_eff(t) = [1−Sum_t'≤tV₂(t)] Sum_t'≤t E(t−t') V₂(t') + Sum_t'≤t E(t−t') V₃(t').
The third chart (now fourth panel of Figure 4) represents the decrease in the R factor thanks to the vaccinations, taking the variation of efficiency with time into account: R_vaccines(t) / R_no-vaccines(t) = [1− Q_eff(t)]², where 1− Q_eff represents the global unprotection from vaccines.

the efficiency of the vaccines declines when the bulk of the vaccinated people received their shots many months ago

Analysis (11 November 2021):

I added three new charts.
The first chart shows that virtually no country fared much better in the 2nd super-wave (1 August 2020 to 31 July 2021) than in the 1st wave. Eastern European countries were much harder hit in the 2nd super-wave, up to 40 times worse than the 1st wave.
The second chart shows that average number of deaths per capita are lower in most countries (with the notable exception of Russia), but the winter months may lead to a rise, unless vaccinations continue to be efficient and the fraction of un-vaccinated people dwindles to a trickle. I admit being surprised that Germany (DE) had half the deaths than France since 1 August 2021, given that their daily deaths are rising exponentially with triple numbers compared to France. But France suffered from a mini-wave in the end of August that more than compensated the current increase in Germany (see the 1st Our World in Data chart above). France shows improvement, because of the mini-wave experienced in August. If the current "5th wave" continues in France, the arrow will go upwards.
In the third chart, one first notices a decreasing trend of deaths with increasing fraction of fully vaccinated people, which is statistically significant (less than a chance in 80 that such a trend would occur by chance [using Spearman and Kendall tests]). One notices that all the countries with over 75% of fully vaccinated people have low current deaths rates. Could this be the magic level that all countries should aspire to reach? This should be taken with caution because:
- Some countries (like Israel) vaccinated early and in fact had a strong wave in September 2021 (see the 1st Our World in Data chart above).
- Some vaccines may be less efficient than others.
- There are too few countries with over 75% fully vaccinated to test this magic level where deaths rates are small.

Analysis (23 October 2021):

France appears to have entered its 5th wave!
- The daily hospital arrivals for COVID-19 have been increasing since roughly 10 October 2021.
- The fraction of positive tests (not shown in the figure) has also increased since roughly 10 October.
- The percentages of positive tests have simultaneously occurred in Germany and Switzerland (as well as the United States), and the 5th wave had begun a few weeks earlier in Belgium and Britain.

Analysis (3 October 2021):

I have not been active on this blog, because the situation is now difficult to analyze, as it depends on several factors that are difficult to predict:
1. the new variants;
2. the government policies;
3. the willingness of the population to be vaccinated;
4. The impact of cold weather.
My prediction of 90 to 100 thousand total deaths by end of April 2021, was quite close, as the number turned out to be 105 thousand.
The situation today is close to that in early October 2020: the numbers of daily hospitalizations, arrivals in critical care, and deaths are actually half of what they were then, but this factor two is small compared to the fluctuations on several months in each of the 4 waves. The now two-thirds of French people fully vaccinated may not be sufficient to prevent a fifth wave in Autumn 2021, because of the coming cold weather, and the slow rise of vaccinations. (I hope my worries are unfounded!)

Analysis (20 December 2020):

I was lucky that my assumption that the French government would ease up the restrictions for the full week of Christmas with no such relief for the 31st of December, was correct.
Alas, my prediction of 30 September that the number of deaths would double to 60 thousand by mid-December was correct (this level of deaths was reached on 18 December), even though it seemed hard to imagine at the time.
The decrease of the 2nd wave begun in early November, was consistent with an R factor near 0.8. But this decrease has hit a plateau in late November (for the hospitalizations), consistent with R near unity. This plateau is difficult to explain. Could it be due to the new COVID-19 strain reported in the United Kingdom, as well as Australia, Denmark, the Netherlands, and South Africa, which might also be present in France for at least a month?
The way things are going, and since vaccines will not be widely distributed before end of Spring, France should reach a total of 90 to 100 thousand total COVID-19 deaths by end of April. It thus seems likely that France will have to impose a 2 or 3 month lockdown as harsh as during the 1st wave to contain the pandemic (with obvious immense stress on the economy and the well-being of the population).

Analysis (20 November 2020):

There latest hospital data appears positive:
- The turnaround of the 2nd wave is more clear.
- It now appears that the R factor since the 2nd partial lockdown is between 0.7 (optimistic) and 0.85 (medium) case, while the pessimistic R=1 case appears unlikely.
But the much-discussed opening of stores on December 1, combined with a one-week lift of travel restrictions during the week of Christmas could lead to as many as 300 daily hospital deaths by COVID-19 until the Spring, i.e. 40 thousand extra deaths by mid-March, making the 2nd wave 50% more deadly than the first.

Analysis (15 November 2020):

There are signs that the 2nd wave is slowing down:
- The trends seem to saturate, in particular the weekly maxima (which are more robust) have decreased.
- The daily hospital deaths have surpassed the critical-care arrivals, which in April was a sign that the peak in deaths was near.
The current R value should become clear by November 22.

Analysis (29 October 2020):

The 2nd wave noticed in September has hit us as strongly as predicted. The R factor is indeed roughly 1.2 (1.23). The hospitals are reaching saturation even quicker than I had estimated a month ago.
The 2nd wave appears to have an increasing R with time between 21 June and 30 October 2020.
A sudden increase of daily hospitalizations and deaths should occur in the first half of January due to the temporary lift of the lockdown for the week of Christmas that I predict the government will allow.
The lockdown will last until:
- end of January at best if we achieve R=0.7 during this 2nd lockdown,
- end of March if we achieve R=0.85 during this lockdown,
- much later if we do not fall appreciably below R=1.
Depending on the value of R during the 2nd lockdown, the one-week lifting of this lockdown will delay the end of the lockdown by:
- one week if R=0.7,
- 3 weeks if R=0.85,
- 10 weeks if R=1.

Analysis (made on 30 September 2020):

Figure 1 indicates that we are witnessing a second wave of the pandemic since early July.
The R factor is roughly 1.2.
If the exponential increase in the arrivals in critical care continues at the same rate (doubling every 2 weeks), hospitals will saturate by mid-November.
Similarly, if the exponential increase number of daily deaths continues at the same rate (also doubling every 2 weeks), the total number of deaths in France will double from 30 thousand to 60 thousand by mid-December. My article was even more pessimistic, by assuming that the R factor would jump to its new value as soon as 11 May 2020, instead of 18 June 2020 assumed here (which fits the data better).

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 June 2020);
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.

Useful links:

Data
- European Center for Disease prevention and Control (ECDC)
- Novel Coronavirus (COVID-19) Cases (JHU CSSE)
- Coronavirus disease (COVID-2019) situation reports (World Health Organization)
Updates
- Our World in Data (Max Roser, Hannah Ritchie, Esteban Ortiz-Ospina and Joe Hasell)
- CovidTracker (Guillaume Rozier)
- Visualisation COVID-19 (Germain Forestier)
- France Info from Santé-Public France
- Johns Hopkins Coronavirus Resource Center
- Coronavirus tracked (Financial Times)
- Wikipedia
- Coronavirus disease (COVID-19) Situation Dashboard (World Health Organization)
- Map of world colored by total deaths per capita (Wikipedia, Dan Polansky)
- Coronavirus dashboard (Avi Schiffmann)
- COVID19 insights (TIBCO Spotfire)
- worldometers
Simulators
- Epidemic calculator (Gabriel Goh)
Analyses
- Why, when and how will the Corona pandemic end? (Avishai Dekel)
- [various articles] (Thomas Pueyo)
- Corona is slowing down, humanity will survive (Michael Levitt, on CalcaList/CTeCH)

Gary Mamon, e-mail: