Leaving the coronavirus lockdown is all in the maths

“Going into lockdown was not, to the chagrin of statisticians, a controlled experiment. Ideally, it would have been very gradually imposed region by region, measure by measure. But in the panic to contain the virus we did not have time to, say, let Wales keep its pubs for a month while Oxfordshire lost its schools.

If we had, we would have a clearer picture of the effect of each intervention. We would know, for example, that closing schools does little while shutting pubs does a lot. Then, when it comes to reopening, we could start with schools and feel relatively safe.”

Tom Whipple, Science Editor www.thetimes.co.uk

From now on, it’s a numbers game. Boris Johnson made it clear that in the weeks to come all that matters in coming out of lockdown is a number known as “R”, the virus’s reproduction rate, and how much each relaxation measure changes it.

But if that sounds like it comes with the comforting certainty of mathematics, the modellers plotting our near future are keen to disabuse you of that idea.

“We don’t have high confidence at all,” says Seth Flaxman, from Imperial College London. “There is a lot of uncertainty.”

R is the reason a virus matters at all. It is a measure of how many people are infected by each new case. If R is above 1, then each new person with the disease infects more than one person and the disease slowly — or not so slowly — spreads. If it is below 1, then each new case results in less than one additional infection and the disease dies out. For measles, R is about 15. For the common cold it is 2.5.

The first problem for Dr Flaxman is that we have only the haziest idea what R currently is for the coronavirus. The second problem is that we have even less idea what effect each of the lockdown measures has on it. The third problem is that as we loosen restrictions, tiny fluctuations in either estimate can have massive consequences.

In February, before Britain had responded to the virus, the R of the coronavirus in the country was somewhere between 2.5 and 4.5, depending on whose estimate you believe. Today we are pretty certain that it is less than 1 — otherwise the NHS would be in a lot of trouble. How far below determines what we do next.

According to the government it is probably between 0.6 and 0.9. Any move out of lockdown will inevitably increase that number — what is crucial is that it does not tip it over 1. We have, to use the epidemiological term, an R budget of between 0.1 and 0.4 — a big uncertainty.

Testing and tracing will give us — again to use the epidemiological term — a bit, but not a lot, of “negative R” to increase the budget. When it comes to wiggle room, that’s it.

The question is, what do we do with it?

Going into lockdown was not, to the chagrin of statisticians, a controlled experiment. Ideally, it would have been very gradually imposed region by region, measure by measure. But in the panic to contain the virus we did not have time to, say, let Wales keep its pubs for a month while Oxfordshire lost its schools.

If we had, we would have a clearer picture of the effect of each intervention. We would know, for example, that closing schools does little while shutting pubs does a lot. Then, when it comes to reopening, we could start with schools and feel relatively safe.

But we did not have that luxury. Dr Flaxman and his team have tried to measure the effect of each broad intervention by looking instead at when they were implemented in each European country. Then from the later changes in deaths, they have backfitted an estimate for their effect on R.

This tells us, for instance, that banning public gatherings — typically involving ten or more people — reduces R by around 40 per cent. A full lockdown reduces it from this lower level by about 70 per cent again. Other measures have less effect. Social distancing cuts it further by between 0 and 25 per cent. School closures are, they think, between 0 and 10 per cent.

However, even if we are certain that these numbers were true at the time — and we aren’t — that does not mean that they are still true now.

Humans, again to the annoyance of statisticians, have a tendency not to be easily defined by numbers. Our behaviour now is different from our behaviour then. We are more careful — which is good. But we also have less to do. Closing schools may indeed have had a modest effect six weeks ago.

Today, though, dropping off their children at a reopened school would be the social highlight of the parents’ (and virus’s) day.

So how can we be certain we can get out of lockdown safely? The answer is we can’t. The truth is we have to view life as a statistician, and accept uncertainty: we open up gradually, then through testing carefully monitor R. If it tips above 1, we close down again.

And as to which of the many possible measures we might choose first, for this gradual opening? It’s a tough call. “On the record,” says Dr Flaxman, “I have no idea. Off the record, I have no idea.”