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Drop in the UK coronavirus numbers

This morning has brought a new The Conversation article by Paul Hunter. As far as I understand his argument, he makes two claims which I disagree with: (i) the UK (and more precisely England and Wales) are very close to herd immunity and so the recent drop is the result of the depletion of susceptible population, and so (ii) the UK is unlikely to see another peak and COVID-19 will become ‘endemic’ as we will see the effect of immunity waning. This post is about what I think is happening with coronavirus numbers in the UK and what are the medium-term perspectives.

Firstly, the context. UK is a heavily-vaccinated country, with nearly 90% adults and nearly 70% of the whole population with at least one dose of vaccine. It has overcome Israel (66%) and is above the average EU (58%) and the US (56%). The fully vaccinated population is slightly lower, 55% in the UK, as compared to, e.g. Israel 61%. Out of European countries, Malta is a record-breaker, with 89% vaccinated and 84% fully vaccinated population.

Despite high levels of vaccination, many European (and non-European) countries have been experiencing a severe outbreak fuelled by the Delta strain. With the estimated R_0 of 5-7 (each infected individual causing on average 5-7 additional cases in a completely susceptible population and in the absence of any control measures), the Herd Immunity Threshold is about 80%-87%. If the vaccine provided perfect protection, we might not have been too far from this threshold, particularly as we already have a substantial “natural” immunity due to 6 million reported cases – and possibly 18 million unreported cases. However, there is enough evidence suggesting that the immunity, whether by vaccination or by disease, is far from perfect – about 30% after a single vaccine and 60-80% after two doses. In other words, it seems unlikely the UK is reaching the HIT at this stage – it might never get there – and so we would expect Delta to spread in the absence of some form of lockdown.

Until recently, the Delta outbreak in the UK conformed to this picture. Starting at the end of May, the number of reported cases in the UK was climbing up exponentially. Israel, which brought the number of cases to a staggering low value of 1/1,000,000, caught Delta in the second half of June and has been growing exponentially since. A similar picture has emerged in the EU and the US – Malta is apparently a slightly different case, with the epidemic driven largely by English language school children.

But then first Scotland and subsequently England and Wales started dropping the cases. Despite an almost complete reopening on 19th July, the cases started plummeting since the 21st. Hunter – and others – associate this drop with reaching the HIT and so predict that we will now see a sustained drop in the infection – despite returning completely to “normality” – followed by low levels of infection in the years to come as the immunity wanes and people become susceptible again.

While this is an appealing picture and can – and probably will – be used in supporting political decisions, I am very sceptical about it. Just to be clear, this scenario might be correct, and I would be very glad to see this happening. But I see another explanation for the recent drop which – to me at least – sounds much more realistic.

Firstly, what we see in the picture is the drop in reported cases. In fact, testing has dropped much more since the 22nd of July, possibly because most testing in recent months have been in schools. The “Trump” doctrine of COVID-19 testing says, “the more we test, the more cases we have”. Conversely, if we test less, we see fewer cases.

A better measure than reported cases is the share of tests that are positive. Not without its flaws, it takes into account both the infection levels and testing intensity. And it shows that while the UK cases are dropping, the drop is nowhere as rapid and deep as for the cases.

Scotland cases; see the drop after 21th June, delayed by Euro 2020 matches

Secondly, there is a timing of the drop. In Scotland school holidays start before England and pupils were back home around 27th June. England starts holidays later, on 22nd of July. The cases started dropping in Scotland shortly after the 27th June – much earlier than in England. The English cases started dropping from 21st July. This suggests that the drop is a result of a rapid decline in the number of contacts. Contrary to what many politicians would like us to believe, transmission in schools has been a very important element of fuelling up the outbreak. Removing this component is likely to bring down the rate of spread.

Thirdly, the drop just does not look right. The very simplified graph in Hunter’s piece is very smooth at the peak. This can easily be understood in terms of the SIR (or SEIR, or even SEIRS) model – the peak us caused by the number of susceptible slowly – and smoothly – declining as they are “converted” into cases. Mathematically it means that the rate of decline should be similar to the rate of growth before reaching the peak – if the peak is caused by the HIT. We do not see it in the data – the drop is much more rapid than it would have been. We have already seen such rapid drops in the past – in the UK, in Portugal, and other places – every time caused by the behavioural changes, not the HIT.

Notwithstanding the fact that Hunter’s plot is a generic SIR plot from Wikipedia and it is unclear what the axes are – why is the starting value of S equal to 350? What are the jagged red and blue lines? Are they the UK data?

So, what about the mid- to long-term predictions? We can look back to the last summer when the numbers also dropped down and kept down until the “second wave” started in September, caused largely by the Alpha strain, and in spring this year, before Delta hit us. Of course, we are now in a different situation, with high levels of vaccination, but – as Israel example is now showing – we are not yet safe.

Finally, Hunter is very optimistic in his SEIRS predictions suggesting that following the outbreak we will have COVID-19 circulating at a very low level. This is possible, but again the history of other diseases points to many counterexamples. Depending on how fast immunity wanes, we might see not only a constant low rumbling of the virus – we might see huge repeating outbreaks, like measles, smallpox, or plague. We might see new strains appearing, like avian or swine flu. There is more to ‘endemic’ diseases than it seems and it is only a precarious ‘equilibrium’ that we might be reaching.

Why is the type of argument presented by Hunter so dangerous? Over the last 18 months, there have been many times when one person or another claimed we had reached the HIT and COVID-19 is just about to become ‘endemic’. Many times – in England, Brazil, India – this has led to relaxing of all rules which eventually has led to renewed outbreaks. I hope this is not likely to be the case this summer.

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