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.

“Freedom day” and herd immunity

A quote from the Politico newsletter this morning, which shows very clearly that we are back to the idea of “herd immunity by infection”:

A government official defended their position to Playbook last night by conceding that millions of people will catch COVID in the next few weeks, but arguing that the vast majority will have only mild cold or flu like symptoms thanks to being double jabbed, and that younger people who have only had one dose of the vaccine are very unlikely to be hospitalized. The hope among government scientists, the official said, is that the explosion in cases, coupled with the vaccination program, will build so much immunity in the population that cases will eventually drop back down and something much more approaching normality can be achieved.


This agrees with the news regarding modelling done by the UK government earlier this year, as reported by Byline Times a month ago:

The Cabinet Office incorporated ‘herd immunity by natural infection’, alongside vaccination, into all the modelling used to develop Boris Johnson’s ‘roadmap’ out of lockdown earlier this year, Government documents examined by Byline Times reveal.


Any increase in deaths in England due to COVID-19 as of today will be a direct result of this political decision taken early this year.

Masks and COVID-19 pandemic

A really good overview of the contribution of masks to suppressing the spread of COVID-19 has just been published in The Conversation. It is a very good article and I thoroughly recommend reading it. In this post, I want to concentrate on one of the seven points that are mentioned there.

Countries that quickly introduced masks – primarily Asian countries with SARS experience – seemed to be much more successful in suppressing the initial outbreak in March-April 2020.


This figure comes from a very interesting paper by Lefler et al, 2020, which analysed data from March-April 2020 and categorised the outcomes of the pandemic (cases, deaths) in relation to lockdowns and mask-wearing. Essentially, this figure shows that countries that introduced masks earlier suffered much lower deaths during the initial period of the epidemic.

This reduction could have been due to other factors than just mask wearing. However, Lefler et al, 2020 actually consider these different factors (like lockdown, obesity, age) and find that mask wearing – or not – was the main factor determining the death rate in these countries (in fact the most significant one).

The authors of this study include a graph that demonstrates that the longer it took for a country to introduce masks, the higher the death rate was:


Here, the start of the outbreak is 5 days before the first case reported, or 23 days before the first death (whichever was earlier) and the duration of the outbreak without masks is defined as the time from the start of the country’s outbreak until masks were recommended or until April 16 (whichever came first).

The line is the linear regression – note the logarithmic scale of the vertical axis, meaning that the differences were actually quite large – about 1,000 times from one end of the regression line to the other. In other words, countries that introduced the mask 12 weeks or so into the outbreak suffered 1,000 times higher mortality than those that started immediately.

Or, each delay of 2 weeks from the onset of the outbreak causes a 10-fold increase in per-capita mortality.

We of course need to be careful in the interpretation of the results. There were certainly many factors that influenced the outcome of the first wave. I have not seen an analysis extending this study to later stages of the epidemic. But, as The Conversation article reports, there have since been multiple lines of evidence showing that the virus spreads through the air (either by droplets or by aerosol) which points to masks as a key way to control.

Why is it so important now to read into this – quite old by current standards – paper? There is a current discussion in the UK on whether masks should continue or not when all other regulations are dropped on July 19th. SARS-CoV-2 is airborne and it is still spreading, so masks should continue to be worn, especially in places of high risk.

Moreover, even where and when it is not compulsory to do so, it should be socially acceptable for those who feel at risk – or those who might be ill – to wear them.

A disclaimer: I do not like wearing a mask, although I have invested in a high-quality one by Airinum having worn similarly excellent homemade masks at the start of the epidemic. But I am really puzzled by such a strong resistance to the idea of mask-wearing. Even in Western countries, we are taught from childhood that we should be doing things that protect us – and others – from risk, even if it comes with a cost. “Do to others what you would have them do to you” is the Golden Rule widely accepted in our culture. How is it then that so many people in the West feel so strongly against mask-wearing?