Coronavirus: What is the R number and how is it calculated?

By James Gallagher Health and science correspondent 18 May 2020

… scientists work backwards. Using data – such as the number of people dying, admitted to hospital or testing positive for the virus – allows you to estimate how easily the virus is spreading. Generally this gives a picture of what the R number was two to three weeks ago…

If the reproduction number is higher than one, then the number of cases increases exponentially… but if it is below one then eventually the outbreak stops. The further below one, the faster that happens… The reproduction number is not fixed. Instead, it changes as our behaviour changes, or as immunity develops…

In other words, Ris an arcane ex post facto constantly varying constant calculated from hunches based on whatever data is available and fed into computer models to help modellers in their travails. Or possibly extracted from computer models. Who cares? As the BBC’s science correspondent says, “scientists work backwards..” If they find it useful, so be it. Explaining it to us mortals over and over what R is is about as useful as explaining the chemical formula of the glue used by modellers who make replicas of the Ark Royal out of matchsticks. We don’t need to know. We look at the results and admire. Or not.

The Imperial College study apparently made its R calculations using information from the British census – good, reliable data no doubt – but how useful is census data for estimating the probability of passing on a virus?

Let’s take as a concrete example three of the earliest clusters identified in France.

1) The first one was caused by an Englishman returning from the Far East who stopped off at a French ski resort in the Alps and infected four other English tourists before returning to his home in Majorca. That’s an easy one. R=4. Or, as far as England is concerned, R=0.

The four infected English people then returned home to England without infecting anyone else. R=0. Average R value =0.8. <1, therefore containable.

Two factors are no doubt at play here which were not allowed for by the French authorities who closed down all ski resorts, or in Ferguson’s calculations:

– Englishmen abroad may share the same chalet, while keeping as far as possible away from other human beings. That’s because they’re English, and the others are foreigners.

– A ski slope is the only other place apart from the United Kingdom where a two metre distance from your neighbour is obligatory.

2) The second major outbreak in France occurred at an Evangelist meeting at Mulhouse, from where it spread as far as French Guyana. Whether this was caused by one R=200 “super-spreader” or a number of spreaders-lite who just happen to like getting up close, joining hands and singing very loud, is an open question. The point is, there was nothing in the data on which the scientific advice was based which would have helped in determining the government’s response. Lockdown came to happy clappy congregations and Trappist monasteries alike, to bare ruined choirs run by the National Trust and the kind of sado-maso nightclubs in vogue in certain political circles, independently of the distancing typically practised by aficionados.

Where was I? Barnard Castle? Surely not. Oh yes.

The third major outbreak in France (possibly the first chronologically – no-one knows) occurred in a village in the north of France near an airfield. This was where the plane arrived which performed the first well-publicised evacuation of French citizens from Wu Han. The evacuees were packed off to a holiday camp in the South of France and no cases of infection were reported. Then cases broke out near the airport. It’s a military airport, which also houses the headquarters of the French secret service. No-one knows why, no-one is asking questions, and R numbers are unlikely to be forthcoming.

That’s enough about France. I recently spent two weeks in England, of which several hours were spent not in lockdown, queueing outside supermarkets. A couple of observations:

1) The English middle classes, despite their expressed love for Europe, have not mastered the metric system. They seem to think that two metres is the length of a cricket pitch. If social distancing was all it’s cracked up to be, we’d be out of the woods by now.

2) Working class men tend to talk loudly and laugh a lot. Working class is cool, as George Orwell didn’t live long enough to say. I noticed this in Tesco’s, where two blokes would stand at opposite ends of an aisle and chat and chuckle to each other over the heads of poor masked expats desperately searching for Bovril. (Where’s it gone? Who’s hoarding it?) They may be taking risks now, but I’ll wager they’ll have developed a healthy herd immunity to all the dire psychological symptoms facing the masked remoaners when the virus is over. (Note to Dominic Cummings – if his team of Nobel prized weirdoes hasn’t already sussed that one out.)

(Note that my observation on the loudness and hilarity of the working class is not only wildly politically incorrect but unsupported by any hard data. How many thousands of hours of sociologists’ time would it take to confirm or refute my assertion – or any similar assertion by Orwell or Mayhew or Marx in his lighter moments? Who cares?)

All this to point out that the data available to Professor Ferguson may have been accurate, but is possibly not the data he needed for the job.

And the same is true, but at a thousand or a million times the cost in research funding, in the case of climate.

I’m sometimes (but not always) a bit overawed by the expertise of some of my colleagues here, in physics, statistics, computer science, risk assessment, etc. If I have any area of expertise, it’s in ancient art history. It’s fascinating to see how people have pictured the world to themselves, and the symbols they have used to attempt to transmit their vision of the world to others, across the ages. The further back you go of course, the more arcane and absurd the symbols seem.

But it helps to see that R, like tau, like alpha and omega, like climate sensitivity, is just symbol.