The elbow that saved Christmas

One day like this a year would see me right

Heading for disaster

In advance of Prime Minister Sunak’s appearance at the UK COVID Inquiry, there’s rightly been much focus on his role in arguing against restrictions in Autumn 2020. Since, despite our best efforts to avoid them, we did end up facing protracted lockdowns in that period it’s become widely accepted that the lesson of the pandemic is that when introducing restrictions (in the words of Patrick Vallance):

you had to go earlier than you would like, harder than you would like and broader than you would like.

In the context of spring and autumn 2020, this argument seems pretty convincing. But there’s actually another time when we didn’t do this, at least in part because of the interventions of Sunak, and things didn’t end in the disaster that was forecast. But I think the reasons for this are slightly subtle and not properly understood by enough people, and we’re in danger of learning the wrong lessons here, so I’d like to explain what I think happened.

The setting is more or less exactly two years ago. On 23rd November 2021, virologist Tom Peacock had tweeted about a “very small cluster of variant associated with Southern Africa with very long branch length and really awful Spike mutation profile”. As we now know, this was the beginning of the omicron era.

While people had perhaps hoped that this new strain might stay confined to Southern Africa for a while, and that the addition of these areas to the UK’s red list on 25th November (only two days after Peacock’s tweet) might keep the variant out, it was already too late. By 1st December, there had already been 22 omicron cases sequenced in England. This was the tip of a fast-growing iceberg: three weeks later on 22nd December, this number was up to 69,147.

The fact that the remorseless arithmetic of exponential growth was combined with such a fast growing variant was terrifying. Just comparing those figures, omicron cases had gone up by a factor of 3,000 in three weeks. A simple calculation says that is more than eleven doublings - implying that omicron had a doubling time of under two days across that period. Despite our vaccination programme, this was faster COVID growth than we’d seen in an immunologically naive population in March 2020, and it seemed like the story could only end in one way.

On 15th December, Independent SAGE had issued an emergency statement calling for a circuit breaker lockdown:

The opportunity for early action has been lost and the time for further delay is over. The situation is so urgent we must take emergency action now and that means it is imperative to reduce contacts. Advice is no longer enough since it does not convey the urgency of the situation. Accordingly we now call for an immediate circuit break to then enable limited mixing from the 25 to 28th December.

Once again, it seemed like the Government had acted too late. How could we have forgotten Vallance’s mantra? It felt like a matter of time before the scenes of December 2020 were repeated: an announcement of strict new measures coming too late, and the second year of Zoom Christmas. Disaster seemed baked in.

Real world results

And yet.

Those announcements never came. And, nasty though it was, we didn’t completely repeat the catastrophe of January 2021. Beds occupied by COVID patients peaked at just under half the levels seen then. That was bad, but some predictions had been much much worse. Daily deaths peaked at just over 200, still too high, but nothing like the 1,200 that we’d seen a year before.

Looking back, it’s possible to dismiss it all as just a silly fuss. It’s tempting to look at a quoted model of 600 to 6,000 daily deaths, and think that the scientists got it all wrong. But it’s worth remembering that was simply one group’s modelling under a high degree of uncertainty (we knew very little about the relative effect of intrinsic spreadability and immune escape for example). Other groups did better: the LSHTM model had a most optimistic scenario of 2,410 daily admissions, not so different to the 2,100 seen at the peak.

Similarly, while certain people will tell you that omicron was a nothingburger, that it was mild, that was to a large extent due to the fact that it met a well-vaccinated population in the UK. For example, in Hong Kong where vaccine coverage in the old was much less complete, omicron caused a “mortality rate of 37.7 per million population that was among the highest in the world during the pandemic” (even the UK’s terrible January 2021 peak was only around 21 per million).

So, what did happen? I believe that the answer is that we got lucky to some extent. Omicron slowed down, because a mathematical quirk meant that our measures could be more effective.

Here comes the maths bit

I think the answer is to do with omicron’s shorter infection time. Suppose we have two variants: one takes 5 days to infect people, the other takes 3. With no measures, imagine that the first has R = 1.5 (each infected person infects 1.5 others on average) and the second has R=1.4.

Imagine we start with 1,000 people infected by each strain and check in 15 days later. The first virus has seen 3 generations, so the number of infected people is 1000*(1.5)^3, or 3375. The second has seen 5 generations, and despite its lower R number this means it has infected 1000*(1.4)^5, or 5378 people. The shorter infection time gives the second virus more chances to spread, and we see it has a growth advantage.

But now suppose we bring in measures that cut peoples’ contacts down by 30%. The first virus has an R number of 1.5*0.7, or 1.05. So now, in a 15 day period, infections would grow from 1000 to 1000*(1.05)^3 or 1,158. Whereas the second virus now has an R number of 1.4*0.7, or 0.98. In the same 15 day period, infections would actually shrink from 1000 to 904.

This is a general phenomenon. Bringing in measures (or the emergence of immunity through infection) will have a bigger effect on the virus with the shorter infection time, and its growth advantage will be reduced.

Back in the real world

So, we can examine what did actually happen. While we didn’t go into lockdown, it is not the case that we did nothing either.

A big part was played by vaccinations. The data is not as accessible as it used to be on the dashboard, but at the start of December 2021 we’d done 97.2 million vaccination doses in England, a month later this figure was 111.9 million. In other words, nearly a quarter of the population got a jab in one month!

Further, the Government announced that from 10th December, we would move to Plan B. This wasn’t as significant as a full lockdown, but it included a return to masking, working from home where possible, and some use of COVID certification to enter large gatherings. All of this would be expected to cut contacts.

Finally, of course, people adapted their behaviour. The reports of omicron numbers were alarming, nobody wanted to be in isolation for Christmas if they could help it, and so I think it’s likely that people behaved more cautiously as the month went on.

We can argue about the relative size of these effects, but perhaps it doesn’t matter. It seems clear that the overall effect of this would be a drop in infectious contacts. If so, and if omicron did indeed have a shorter infectious period, then we would expect that its growth advantage over the previous strains would be eroded.

I’ve written extensively about how a constant growth advantage would lead to points lying on a straight line when plotting variant shares on so-called logistic axes. Well, if we examine the share of omicron cases both in London (blue) and England (red), we can see that this happened for a while, but then the points dropped off the straight line.

If we had kept on the straight line, and omicron’s growth advantage had stayed the same, then I think some of the doomier predictions might have come into play, and stricter measures might well have been necessary. As it was, I believe that the shorter infection time (for example this paper estimates around 3 days for omicron, compared with the 5 days or so observed for alpha) meant that the measures we did take had more chances to work, and could therefore be more effective.

In other words, you have to plot the data exactly the right way (percentage shares on logistic axes, not looking at overall numbers), but if you do then you can see the elbow on the graph around the time of the Plan B measures, which meant that Christmas 2021 could go ahead more or less as we’d hoped.

Perhaps we were lucky in this sense? It wasn’t a complete surprise that this was a possibility - the LSHTM paper I mentioned about had explicitly said that “If the generation interval of Omicron is shorter than 5.5 days, then Rt would be correspondingly lower” - but after the couple of years we had been through previously, who is to say that we didn’t deserve some good luck for once?