Gro-Tsen Profile picture
5 Nov, 32 tweets, 7 min read
✽ An important clarification which I feel I have to make concerning “herd immunity”, its value and more importantly, its definition. The point is, the basic reproduction number R₀ describes a population that is immunologically AND sociologically “naïve”. •1/32
In other words, R₀ describes (the number of individuals who will be infected, on average, by one infected individual inside) a population which has never come in contact with the virus, but doesn't even know about it, care about it, or take any kind of precaution. •2/32
Consequently, if we apply the formula 1 − 1/R (which itself has many caveats and limitations, but it's not the point I'm trying to make here) to this number R₀, we are computing a herd immunity threshold for a naïve population as described in the previous tweet: … •3/32
… in other words, this — let's call it “unconditional” — herd immunity threshold is the proportion of individuals who must become immune for the disease to no longer spread in a population which takes NO precautions to protect itself, and hasn't even HEARD of the disease. •4/32
For covid, this R₀ was estimated at around 3-ish (or actually anywhere from 2 to 6), back in March, from the initial January–February outbreak in Wǔhàn, in a population which was, indeed, arguably “naïve” at the time. •5/32…
But ✳︎SPOILER✳︎: quite a few people around the world have heard about covid-19 by now. 😐 •6/32
Now if we consider a population which already has partial immunity and/or is taking any kind of precautions against the disease (e.g., traveling less, wearing masks, or anything of the sort), we have a different reproduction number R₁<R₀, … •7/32
… and of course the number of people who must be made immune in this non-naïve population in order to stabilize the disease is 1 − 1/R₁ (again with many caveats and limitations), NOT 1 − 1/R₀. We might call this “conditional” herd immunity: … •8/32
… all this means is that it doesn't have to be either pure full unconditional herd immunity or pure interventions which stabilize the disease: it can be any combination of them. (This point should be blindingly obvious, but some people seem to fail to grasp it.) •9/32
“Conditional” herd immunity means that some combination of immunity and other measures stabilize the spread of the disease: it's not a well-defined point, of course, it's a spectrum with unconditional herd immunity at one end and lockdowns at the other. •10/32
Essentially ANY place where the disease is no longer progressing in an exponential factor HAS attained some form of conditional herd immunity, meaning that some combination of collective immunity and other measures are stabilizing it. •11/32
Now if you compute the herd immunity threshold with the 1 − 1/R formula by plugging in R=R₀, which is the case if you think it's around 60% (namely for R₀=2.5) it means you're aiming at stabilizing the disease using ONLY collective immunity, NO further measures. •12/32
(Note only no further measures, but even going as far as assuming your population doesn't know about covid, doesn't care about covid, will take no steps to protect itself against covid, and behave in every way as the “naïve” population for which R₀ was measured.) •13/32
This is very much a straw man argument, then, because I don't think, even with a vaccine, anyone would seriously suggest this “let's just completely ignore covid and forget it even exists” approach, which is the one for which you would need to immunize 1 − 1/R₀ people. •14/32
I therefore call it a straw man to use the 1 − 1/R₀ value (around 60%) for herd immunity threshold except if one made sure the person one is arguing with is indeed defending the “completely ignore covid” approach outlined in the previous tweet. •15/32
In any other case, one must use the formula 1 − 1/R with a value of R that realistically describes the population being considered, in the country or area being considered, with the level of protective measures they are willing to take (especially in the long run). •16/32
Now one of the striking properties of the covid pandemic is how R(t) fell very rapidly even before any kind of measures were imposed “from above” (e.g., lockdowns). E.g., this graph taken from… (archived version of…‌) … •17/32
… shows how France's reproduction number evolved with time, and dropped from around R₀=2.5 down to 1.5 before lockdown started on 2020-03-17. Since then it has hovered between roughly 0.75 and 1.5 (it was around 1.2 just before second lockdown). •18/32
In fact, it's been fairly stable as of recently around 1.2:… (no particularly big jump either up or down as a result of anything). •19/32
Other sources report more variability in R(t), whose computation is delicate and fraught with uncertainty, see — but at any rate, it's always in the 1.2-ish range for European countries right now (and I mean, even before second lockdowns). •20/32
In fact I don't remember seeing a country with R>1.5 more than briefly since covid really became a global pandemic, and certainly not recently. (I don't spend my time looking at these graphs so I may have missed some, though. But they're certainly not typical.) •21/32
Now the REASON why R has fallen so rapidly from R₀~2.5 down to values in the 1.0 to 1.5 ballpark range is unclear. It could be due to many things (less mobility, masks, partial immunity, or a host of other things — nothing very satisfactory), but that's not my point. •22/32
My point is that the R₀ value of 2.5 (or even higher!) and the corresponding “unconditional” herd immunity threshold of around 60%, are completely irrelevant except as straw man arguments or if talking to a deranged person who would argue as in tweet 14 above. •23/32
In the real world, the relevant value of R is somewhere around 1.2, perhaps 1.1 to 1.5, depending of course on exactly what measures are deemed acceptable in the long run, giving a “conditional” herd immunity threshold between 10% and 30% maybe. •24/32
(And of course, this is applying the 1 − 1/R formula which still has a lot of caveats which I don't want to get into in this thread, but one expects the actual value to be lower if any kind of heterogeneity is involved, e.g., between urban and rural areas.) •25/32
This is not to say the formula 1 − 1/R₀ is wrong, or that people who refer to it are wrong. But it is to say that it is deeply misleading unless you are advocating (or speaking with someone who is advocating) a “let's completely forget that covid even exists” strategy. •26/32
Essentially this is a false dichotomy argument which consists of assuming that if somebody is arguing against lockdowns then they must be in the “completely forget that covid even exists and do nothing” (straw man) extreme. •27/32
This makes me particularly angry coming from epidemiologists who should know better, e.g., Fontanet and Cauchemez in their now infamous comment “Covid-19 herd immunity: where are we?”… — which uses R₀~2.5 WITHOUT SO MUCH AS A COMMENT. •28/32
And sadly, the upper bound of their (already pessimistic for many other reasons) 100k–450k death range for France to attain (unconditional!) herd immunity has been reused by French president Macron to justify the second French lockdown: … •29/32
… thus using the false dichotomy mentioned in tweet 27 above: “if we don't have this lockdown, this means we're pursuing unconditional herd immunity [←false dichotomy], which will cause 400 000 deaths [←upper bound of an already pessimistic interval]”, … •30/32
… as if not having this lockdown automatically entailed giving up on everything that has been done to limit the spread of covid. This is just plain silly. A more reasonable estimate uses 1 − 1/R₁ with R₁~1.2 observed in France since mid-July: •31/32
Of course, all of this is nothing that I didn't already write in this old thread back in April. But I thought relevant to rewrite it now in a slightly different manner. •32/32

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More from @gro_tsen

26 Oct
Bon, je me suis enfin sorti les doigts du c😶l pour faire un calcul d'espérance de vie perdue par les morts covid en France à ce jour:
⁃ âge moyen des décès hospitaliers: 80.5 ans,
⁃ espérance de vie moyenne¹ des décédés: 11.4 ans.

1. Sans tenir compte des comorbidités.
OK, «espérance de vie des décédés», c'est ridicule. Vous me comprenez: celle qu'ils avaient a priori à leur âge+sexe.

Fine print: j'ai procédé en supposant la fonction morts(âge) continue affine par morceaux pour obtenir les totaux par dizaine d'années publiée sur Géodes.
J'ai intégré ça contre l'espérance de vie publiée sur… et… pour les âges élevés, elle aussi rendue affine par morceaux.
Read 8 tweets
26 Oct
Catalogue de mesures envisagées (élargir le couvre-feu, obliger au télétravail, interdire les longs déplacements, fermer les écoles, fermer d'autres lieux publics…), mais comme d'habitude, rien comme «réquisitionner des chambres d'hôtel pour permettre aux fragiles de s'isoler».
(Sans parler de l'option «ne rien faire de plus», qui devrait au moins être sur la table avant toutes les mesures répressives qui n'ont fait preuve que de leur coût et pas de leur efficacité.)
«Mais ouin! Si on laisse le virus passer, on ne peut pas protéger parfaitement les personnes âgées et vulnérables.» Oui, alors parce qu'on ne peut pas les protéger parfaitement, on n'essaie même pas un tout petit peu …
Read 4 tweets
25 Oct
Perhaps the most frustrating thing in this whole pandemic is how impossible it is to find reliable and readable information about public health measures taken in various places (lockdowns, school and business closures, curfews, mask mandates, etc.). •1/8
That we have unreliable and often contradictory data concerning the virus itself is understandable. But concerning our OWN public actions in response to it, information ought to be near-perfect! Instead, documentation is disastrous. •2/8
I live in France and I can't even keep track of the rules which apply here. They change twice a week and from place to place in a mad, incoherent mess. There isn't even a government Web site recapitulating them all (we're all supposed to read the law, I guess). •3/8
Read 9 tweets
25 Oct
There's something really fishy going on with “effective reproduction numbers” in various analyses of this pandemic. And I'm not talking about predicting the future, I'm talking about analysing the past. Here we see a claim of R~3 for Belgium. •1/21
On the other hand, researchers at the Centre for Mathematical Modelling of Infectious Diseases have a web site computing R(t) for many countries, and their estimates for Belgium never went above 1.5 in the computed time frame:… •2/21
Now briefly speaking, computing R(t) depends on two things: the exponential rate of growth r (=logarithmic slope, =logarithmic derivative) of the number of new cases, and temporal data on infections, notably the “serial interval” and its distribution. •3/21
Read 23 tweets
24 Oct
Il y a 160 ans, les soldats français et britanniques, pour punir la Chine de refuser qu'on lui deale de l'opium, ont pillé puis détruit ce qui était certainement une des plus grandes merveilles de l'art palatial et horticole, le Yuánmíng yuán ou Palais d'été des Qīng.
Victor Hugo écrit assez bien son indignation: «Les artistes, les poètes, les philosophes, connaissaient le Palais d’été. […] Cette merveille a disparu. Un jour, deux bandits sont entrés dans le Palais d’été. L’un a pillé, l’autre a incendié.» (‌…‌)
Cette date d'octobre 1860 est évidemment bien connue des Chinois, mais je me demande à quel point elle l'est en France et au Royaume-Uni. Elle est pourtant, et continue d'être, géopolitiquement importante.
Read 5 tweets
23 Oct
Heureusement que le ridicule ne tue pas, sinon ce gouvernement serait face à une hécatombe bien plus importante que celle due au covid.
Mais bon, soyons compréhensifs, peut-être qu'il s'agit d'un simple malentendu: les préfets ont pris le Journal Officiel pour un recueil de blagues et cherchent à détendre l'ambiance en publiant celle qui fera enfin rire les Français dans cette période difficile.
Non mais faut vraiment lancer un petit concours «imaginez la prochaine restriction ridicule dans votre département». Attention, pour être admissible à concourir la mesure proposée doit être totalement inefficace et doit inclure une amende de 135€!
Read 4 tweets

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