My blog on the spread of Covid-19
Regional analysis of COVID-19 in France from fit of hospital data with
different evolutionary models
(13 May 2020, version 4: 17
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 prehospitalized 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 y 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
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)
comprendre la pandémie, les courbes valent mieux que
les avalanches de chiffres.
Reproduced in weekly magazine La Tribune
and monthly Santé Magazine.
Progression in France
- Data from Santé Public
automatically extracted daily from the
- The points are the 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 was constant
before the lockdown and another constant between the lockdown of 17 March
2020 and the date of 10 June 2020 (the national lockdown ended on
11 May 2020). After 10 June 2020, the models assume that all regions share
the same constant R value
after 10 June 2020, according to 4 different scenarios for R. The
curves beyond 4 May 2020 are extrapolations from the models.
- 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.
- The figure is automatically updated daily.
Progression in different countries: (until 18 June 2020).
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 (doubling every 3 weeks), the total
number of deaths in France will double from 30 thousand to 60 thousand by
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 10 June 2020
assumed here (which fits the data better).
- Data automatically extracted from the
Center for Disease Prevention and Control (ECDC)
Note that all charts use logarithmic vertical axes, where the ticks increase
multiplicatively (instead of additively).
The black segments indicate the doubling time.
The filled circles indicate the time of full national lockdown.
The flattening of the curves at the latest times of the doubling time
charts is an artifact of the method used to measure these times.