Counting is one of the most fundamental tasks in epidemics. If you don’t know how many cases there are, you’re lost. It also seems to have been an early casualty in many countries in the current pandemic. In this article, I try to find the answer to a simple question: how many cases of Covid-19 occurred (were diagnosed with a positive PCR virus test) in the UK on 22 May 2020?

Gathering data on infectious diseases is the task of the public health authorities. In the UK, there’s no unity, and each of its four nations has its own: Public Health England (PHE), Scotland (PHS), Wales (PHW) and Northern Ireland (PHNI). According to those, on that date there were:

• 698 cases in England
• 366 cases in Scotland
• 106 cases in Wales
• 28 cases in Northern Ireland (a rolling average, apparently)

which comes to a total of 1198 if my fingers and toes have got it right. PHE declared that there were 351 deaths reported in the UK on that day.

PHE also has a separate site on which it reports test results, and provides consolidated figures for the UK. These are among the most complex, in that tests are broken down into four ‘pillars’. Here, I’m concerned with the first two of these, only they report a mixture of different tests. Pillar 1 includes results from patients in hospital who are by definition ill, plus those from key hospital workers who may be asymptomatic. Pillar 2 includes those with symptoms outside hospital care, and those without any symptoms who have asked to be tested. Not only that, but PHW reports both Pillars in the same total, without splitting, while the other three give separate numbers.

The total for that day for the UK’s Pillar 1 positive test results (including Wales’ Pillar 2) was 1357, and that for Pillar 2 (excluding Wales) was 1930, giving a grand total of 3287 positives, which includes results from people without symptoms or any other evidence of Covid-19 infection.

The next reporting tier up is the ECDC, but their figures operate a day late, so I here refer to those for 23 May. On that day, the UK reported 3287 cases and 351 deaths, and that was passed up to the top of the chain at the World Health Organisation, as the official totals for the UK.

So from those reports, there could have been 1198 or 3287 fresh cases in the UK, of which anything upwards of 698 might have occurred in England. If that spread isn’t enough for you, Paul Birrell and others of the Joint PHE Modelling Cell at the MRC in Cambridge have tried to take into account under-reporting by people, asymptomatic and presymptomatic cases, and give for 22 May a median estimate of 17,500 cases, with a range from 13,600-22,300 for England alone.

The answer to my original question is that the number of cases of Covid-19 which occurred in the UK on 22 May 2020 most probably lies between 1,198 and 22,300. With the operative word being lies.

The ‘R number’

If we can’t tell how many cases occurred on any given day, what about the figure that government and press have seemingly discovered, the ‘R number’? After all, if that’s less than 1, Covid-19 is on the decline and will eventually die out, won’t it?

The sad fact is that there isn’t such a thing as the R number, but several. The most fundamental is R₀ (capital R with a subscript zero). This is the basic reproduction rate for any given infection in a fully susceptible population, and for Covid-19 is of the order of 3.8, although some have claimed that it’s significantly higher.

What we’re most interested in is the effective reproduction rate in a given population at a specific point in time, sometimes referred to as Rt. That is normally estimated from the rate of change in fresh cases, so if you’re not fairly confident of how many cases are occurring, Rt is going to be no more than a guess, which is why for the UK and its regions there are several differing estimates of Rt at any time.

Change and comparisons

One way of addressing problems like these is to get the best estimate, and hope that any underestimation and errors are at least going to be fairly consistent over time. That might have worked at one time for the UK figures, had the basis for them remained unchanged. Unfortunately, it has changed several times, and in recent weeks increased testing has made those figure impossible to compare with those from, say, March or April, when far fewer tests were performed mainly on patients in hospital.

Here, I have looked only at figures from the UK. Can we make international comparisons, as so many of us are wont to do in some sort of league table of which government has managed the pandemic best?

Only when you understand in the same sort of detail how comparable each nation’s reported figures are, can you start trying to compare. As testing regimes are wildly different across different countries and have changed during the course of the pandemic, the basic figures aren’t comparable. Nations have also applied large corrections, and many have used various tricks to try to minimise the numbers of both cases and deaths which they report.

Just over a century ago, the great Influenza Pandemic which followed the First World War was recorded and reported manually, in pen and ink. It looks as if, with the aid of computers and modern numerical and statistical methods, records from the Covid-19 pandemic will be even less reliable.