May 15, 2020, by Brigitte Nerlich

What R we talking about? Pandemics and numbers

The Covid-19 pandemic has brought us many new words and phrases, words and phrases that are reshaping our lives, such as ‘social distancing’, furlough, WFH (working from home), which I always read as WTF, zoom meetings, PPE and so on. It has also brought with it lots of numbers and graphs and other mathematical and/or modelling phenomena.

Numbers have always been part of disease outbreaks, epidemics and pandemics, especially numbers of cases and numbers of deaths, and the graphs plotting their ups and downs. More recently, there have also been mathematical models. So-called quantitative epidemiological modelling became a topic of discussion during the 2001 outbreak of foot and mouth disease in particular, when models decided which animals were to live or die.

Knowing your Rs from your elbow

However, this pandemic brought something else to public attention on top of numbers, graphs and models, namely a rather complex mathematical number which has now become the emblem of the disease and its management. That number doesn’t look like a number. It looks like a letter. It is R, called the R number, R rate, R level… – with other cryptic letters and numbers added, such as R_0,R_e, R_t, and so on.

I am not a scientist, but after talking with some, I have devised this ‘definition’ (all mistakes my own): The R number comes in two forms. The basic reproduction number R₀ is the average number of people that a person with a virus would pass it on to, all other things being equal. This is a property of the virus and its host and it doesn’t change over time. It takes a larger value the more intrinsically contagious the virus is. The effective reproduction number, R_e, or its value at a given time, R_t, depends upon various circumstances such as how many people are immune and how much social contact people have. What follows from that is that isolating people can have the same effect as vaccination.” (And here is a longer and more extensive explanation by Philip Ball; added 21 May, 2020)

As you have all heard by now from the news: If the R value is one, each carrier of a disease passes the virus on to one other person, meaning the prevalence of the virus will stay at the same level. If the value of R falls below one, it will decrease.

Bringing down R has become the new ‘flattening the curve’. But how did politicians talk about this important topic?

A tale of two Rs

Boris Johnson

The Prime Minister Boris Johnson introduced R prominently on 30 April. At one of the daily press conferences he said the following:

“And so to avoid that disaster our fifth and final test is that nothing as I say we do should lift the R or the reproduction rate of that disease back above one…And before I hand over to Patrick [Vallance] I am going to ask for a short explanatory clip about the one… And before we come to that clip, let me just emphasise that keeping the R down is going to be absolutely vital to our recovery, keeping the reproduction rate of the disease down, and we can only do it by our collective discipline and working together”. You can see the clip here, at about 9.15 minutes in – this is quite informative, but not spoken by the PM.

Angela Merkel

I noticed that people in Germany, in this case my 93 year-old father, started to talk about R about a month ago in the context social distancing. This happened especially after a speech by the Chancellor Angela Merkel in which she explained the significance of R in quite some detail and, most importantly, in a way that lay people can understand – good science policy communication in action. You can watch her explanation here. I don’t really want to repeat that. I just want to stress one thing that she made clear: little variations in R can have big effects, for good or for ill.

In an article about Merkel’s speech we read something that is becoming relevant now: “As societies begin to contemplate how to re-start their economies after weeks of shutdowns, epidemiologists have urged a multi-cycle strategy of ‘suppression and lift:’ a regimen of relaxing and tightening social distancing measures to fine-tune them, so that they are just right for a particular population at a particular time.”

That’s the stage the the UK government thinks we have reached about now, but we don’t hear about suppression and lift, we hear instead about ‘being alert’ and ‘common sense’ – but that would be another blog post/rant. (The Independent Sage Report, which has just been published, has more on suppression)

Back to Boris

On Sunday 10 May Boris Johnson gave an address to the nation which referenced R again. R became part of two, to put it charitably, ‘lay-friendly’ ‘explanations’, one a pseudo-equation, the other a pseudo-graph. Both were much lampooned on twitter the following day. They were a failure in science policy communication.

On Facebook, Gareth Roberts, a biology teacher, wrote the following: “Thought it would be fairly sensible to assess the ‘Boris does Science graph’ in the same way we would a GCSE or A-level student”, and the result is splendid. @trishgreenhalgh tweeted it out and it went a bit viral (Thanks to @GarethEnticott for helping me find out more about that image) Oh, and what’s Gareth’s overall assessment? “This work falls well below the standards required to meet your target grade. This is becoming a recurring theme of my feedback to you.”

R for dummies

When seeing and hearing Rs everywhere, I wondered whether there was something like R for dummies… and of course there is, but only about R as a computer language! However, not all is lost. I found two articles, one thread and one interactive game which might help. But there is certainly more out there!

An article in the BMJ (HT @RRITools) that sets out R very clearly, so that politicians can understand things better.

A short article in Wired explains R well, and all the caveats around it!

A more elaborate thread by epidemiologist Adam Kucharski goes into more detail.

And then there is this interactive ‘game’: “What Happens Next? COVID-19 Futures, Explained With Playable Simulations” 30 min play/read, by Marcel Salathé (epidemiologist) & Nicky Case (art/code) – have a go, play and LEARN!

The origins of R

Now, it turns out that Kucharski is the author of an aptly timed book entitled The Rules of Contagion: Why Things Spread – and Why They Stop, which came out at the beginning of this year. The blurb reads like this: “A deadly virus suddenly explodes into the population. A political movement gathers pace, and then quickly vanishes. An idea takes off like wildfire, changing our world forever. We live in a world that’s more interconnected than ever before. Our lives are shaped by outbreaks – of disease, of misinformation, even of violence – that appear, spread and fade away with bewildering speed.” That sums things up nicely!

I was looking at some media reporting about R when I found a review of Kucharki’s book by Steve Bleach in The Sunday Times, published on 16 February, that is, before R entered common consciousness! It starts like this:

“How many of us are going to contract coronavirus? The answer – or, at least, the best means we have of trying to calculate it – started taking shape as long ago as the 1950s, when a researcher at the London School of Hygiene and Tropical Medicine wrote a paper on the control of mosquitoes. Hidden away in the appendix was a novel idea about disease transmission: if you modelled what would happen when a single infectious person arrived in a population, it might give you a way to predict how serious an outbreak would be.

Twenty years later, a mathematician called Klaus Dietz picked up on the idea. What if you established the average number of people that a new case would infect? Call it the reproduction number, or R. You could then calculate how fast the disease would spread, how many people would catch it and, if you could intervene in a way that reduces R, how effective measures to fight it might be.”

So that’s where R comes from I thought! It might just be a letter/number, but it is hugely important. As Bleach says: “Suddenly, the R number looks less like an academic device and more like a matter of life and death. Coronavirus rates somewhere between R1.5 and R3.5, on current estimates [that was February, 2020]. That sounds like a small range, but as Adam Kucharski’s book points out, it has huge consequences.” (highlighted by me)

The future of R and of us

For something that is a matter of life and death, the science communication around it needs to be flawless, or at least try to be. One ingredient in good science communication is ‘trust’. Angela Merkel explained R in a way which implied that she trusted people to be able to understand and then act upon complex information. She didn’t dumb down R; she was clear about it and its implications. And she communicate in a context where actions that could ‘lower R’ were made possible through intensive research, testing, tracing, transparency, good hospitals  etc etc. (This does not mean, however, that everybody trusted her, see here)

This was not the case for the UK government, where science communication was poor and the context was poor too. There was talk about people using their ‘common sense’, which might imply trusting people to do the right thing, while at the same time not providing them with the opportunities to use it – namely clear and non-contradictory information, sufficient PPE, safe infrastructure and so on.

Trust in science and government has to be built into people’s life; it can’t be talked into people’s lives. At the moment this is not happening here in the UK. In such a context even good science communication, including engagement and dialogue, can only achieve so much. Words matter, numbers matter, but worlds matter too. To build better worlds we need better politics, not only better science and better science communication. Only then can trust be achieved and science communication work.

In the pseudo-graph mentioned above, it is assumed that “R will remain below 1 despite it only dropping to 0.9 after six weeks of lockdown“. But as Gareth Roberts asked: “Do you think it is realistic to assume R won’t rise above 1 when we reopen schools, workplaces, bars, restaurants and shops?” As the Independent Sage Report points out (p. 22): “Any easing of restrictions needs to be accompanied by not only effective, targeted messages, but changes in the physical and social environment that enable the key behaviours to suppress transmission”.

PS 3 July 2020: For a good explanation of R, read this article in Nature: https://www.nature.com/articles/d41586-020-02009-w

Image: Flickr, David Goehring

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