R and why we need to keep social distancing

My previous posts covered why we had to lockdown when we did, how we know it worked, and why we are easing now. That brings us to the present where we are being told to keep R (the average number of people that one person with COVID infects) below 1 to avoid a second peak.

So let’s get straight to it. Lockdown is easing and COVID-19 is still here, so to avoid a second lockdown the two main questions are:

1) What do we actually need to do?

2) How do we know if we are doing enough?

Here’s my best interpretation of the answers, building on the key ideas from Post 5 that death on average occurs ~3 weeks after COVID infection, and that COVID will continue to spread in the same way it did before lockdown. 

1) What do we actually need to do? 

Unfortunately I think the chain of communication from Experts -> Politicians -> Media -> Us makes things slightly unclear. The party line is “Stay alert – control the virus – save lives”… Great, thanks… What does that actually mean?… Post 5 contained a rough calculation based on the fact that the peak in infections would be ~3 weeks before the peak in deaths:

This back-of-the-beermat maths shows that our change in actions around the time that lockdown started immediately caused COVID infections to decrease (others appear to also have this conclusion). This is where remembering that COVID will continue to spread in the same way is so important: if you do what you’ve done, then you’ll get what you’ve got. 

The way we acted before lockdown meant R was bigger than 1 as the infection was spreading

The way we acted after lockdown meant R was below 1 as the infection was receding

So, the way we need to act now to keep R below 1 is similar to the way we acted AFTER lockdown started, not before it. 

We should expect that R will rise as we allow more social mixing, but as long as R remains below 1 we are still in the right zone. So while we increase daily activity to get the economy going we need to maintain, or even increase, our level of social distancing, the hygiene, the hand-washing, the not-touching-your-face (god I miss touching my face), the masks, etc, from during lockdown. Full NHS guidance is here. This is what I think “stay alert” was meant to mean. I think they meant:

Don’t stop doing what you’re doing* – it’s working!”

(*Unless what you were doing was checking your COVID-19 infection hadn’t compromised your eyesight by going for a 60 mile drive. That makes you an asshat.) 

2) How do we know if we are doing enough? 

The government said they will let us know if we need to tighten restrictions, but from the multitude of numbers that get thrown at us daily, which one should we pay attention to? The key here is to think about the timeline of an infection, this goes:

  1. Infection
  2. Symptoms
  3. Hospital admission
  4. Death

So, if R goes above 1 the order we will see this effect is:

  1. Positive tests (ideally)
  2. Symptom reporting
  3. Hospital admissions
  4. Deaths

So, as hard as it is, we need to not look at the death toll as the measure of our current success, as the ~3 week timeframe to death means that we won’t see a change until ~3 weeks after we have relaxed too far. Think of it as like getting the results back from an exam we failed 3 weeks ago, it’s too late to change the result at that point – and importantly we likely also failed an exam every day for 3 weeks while we waited for the result… The most tragic outcome of this is that if we only act when the death toll starts to increase, then we can expect the deaths to continue increasing at the same rate for another ~3 weeks. This is exactly what happened when we locked down March 23rd.

Frustratingly, R also has a delay before it changes… Remember R tells us the average number of people that one person with COVID infects, so you could write a rough equation for this that would be:

R x number of old cases = number of new cases

So to actually calculate R, you would just rearrange this to:

R = number of new cases/number of old cases

Therefore, to actually get a value for R, you need to have a value for both number of old cases AND number of new cases. This is where the problem comes, because you have to wait for new cases to appear before you can actually calculate R. And by that point, R is only telling you what the spread was like at the time of old cases… Basically, R tells us what the spread of COVID WAS like, not what the spread currently IS like. The delay in R is apparently ~2 weeks, so although R is the key number in all of this, it is not the actual number we need to watch to know if we are currently doing enough…

As the fastest readout of our current situation, we likely have to gauge our current success based on testing results (hence the WHO’s “test, test, test”). Given testing is quite limited in the UK and possibly also still hospital-focussed, we may have blind spots or may not be spotting new outbreaks (e.g. no new cases in London). Symptom reporting apps such as Zoe can give a much larger sample size than tests (currently 3.7 million per day) and should be the second thing to increase ~4 days after a COVID resurgence. Sorry to keep saying it, but why not get contributing to this if you aren’t already? It takes ~10 seconds per day and may be a vital means to spot a second outbreak early. It’s also worth noting that symptom reporting apps are complimentary to contact tracing apps, they are not the same thing – as an example, symptom reporting gives us an idea of how hard it is raining outside, contact tracing would tell you that you might have got wet when you get home… Testing analysis will undoubtedly be complicated by changes in test numbers and uneven distribution (see Posts 3 and 4) – as the news mainly reports the number of cases, don’t be too surprised if we see a shift in government policy before the effect is really clear to us. Take home message here though:

The first sign we are not doing enough should be an increase in the number of cases from testing, the second sign should be an increase in symptom reporting.

Next time I’ll write about the new COVID treatments we see in the news, when we could start to get excited by these, and when we should take them with a pinch of bleach…

7 thoughts on “R and why we need to keep social distancing

  1. Hi tom , nice to read some sencible and knowledgeable breakdowns on whats actually going on . I’ve been reading some newspapers, not the crap red top tabloids , i like the guardian best . Also got two science mags on my feed so i can get slme proper information . Me , i think the government mishandled it prety much from the start and are just giving us B S . I make my own mind up based on gut instinct and as many true facts as i can get , so thanks for your fact based blog . Best wishes Bri . Keep safe .


    1. HI Brian, glad to hear it made sense! Yeah, I’ve seen a couple of amazing pieces in the Guardian written by scientists who are on the SAGE panel and they’re definitely the ones to listen to on this. The government undoubtedly ballsed this up – and I really pray they’re not about to do it again – but I’m trying to keep the blog focussed just on explaining the science as much as possible. Personally I’ve found that viewing facts through the lens of ‘there must be someone who actually knows what they’re talking about, even if the expert advice gets mangled on the way through the government” has been really helpful in trying to figure out what may be going on. The interesting thing I think is that experts globally seem in pretty tight agreement on how we should act, so the differences between say the US/UK and New Zealand/Germany, would presumably be coming from the government and how much they listen to that expert advice… And as someone in the government once said, we’ve had enough of listening to experts…
      Stay safe and hopefully see you some time soon,


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