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expert reaction to latest R number and growth rate estimates published by the government

The government have published their latest estimates for the COVID-19 growth rate and R value.


Dr Yuliya Kyrychko, Reader in Mathematics, University of Sussex, said:

“The current R number is puzzling and appears to be somewhat in contradiction with the ONS survey showing a rapid growth of cases.

“It’s worth remembering that calculation of R number is done with a few weeks delay, and is based not just on the number of positive cases but also on deaths and ICU admissions.

“While the rate of infections is accelerating for a number of weeks, and hospital admissions are usually lagging behind due to the nature of COVID progression, and so do deaths, that can potentially explain why the R number is lower this week.

“At the moment,  hospital admissions are rising quite fast, which should be reflected in a higher R number in a few weeks’ time.

“Growth in cases does not mean that the R number should necessarily be changing though it is most probably higher than the one published today.

“To give an example, if the R number is 1.2, that means each person infects 1.2 other people, and they infect 1.2 other people and so on, so the number of cases will grow exponentially but the R number will remain the same.”


Dr Konstantin Blyuss, Reader in Mathematics, University of Sussex, said:

“A rapid growth in positive cases combined with growing hospital admissions suggests that the real R number is higher than the one released this week.

“The updated R number takes into account the situation from a few weeks ago, and as such, is not really reflecting the situation today.

“It’s worth pointing out a large margin in increase in daily growth rates, which is similar across almost all regions of England, and suggests that the infections are rising across the country, unlike localised outbreaks that were happening over the summer.

“ONS survey results also suggests that the infections are rising across all age groups, and will inevitably reach the most vulnerable individuals.”


Prof Matt Keeling, Professor of Populations and Disease, University of Warwick, said:

“R is linked to the growth rate of the epidemic.  High R means high growth rate and a steep rise in infection.  Low R (but R still above 1) means a lower growth rate but infection is still increasing.  Cases are still doubling, but maybe not quite as quickly as they were – although any change is still within the confidence bounds of last week, so the change is not statistically significant.

“Best analogy I can give – R is how hard you are squeezing the accelerator, if you come off the accelerator slightly you still keep traveling along the road, and similarly cases keep increasing.  (We are nowhere near applying the brake, which would be R<1).

“[Note: please don’t take the analogy too far, the laws of physics are not the same as those governing the outbreak!].”


Prof Kevin McConway, Emeritus Professor of Applied Statistics, The Open University, said:

“Regarding the official Government figure, it’s not necessarily the case that R has gone down.  This week’s range is 1.2 to 1.5.  That means that they’re saying that R is somewhere between 1.2 and 1.5 (and they don’t know it more precisely than that).  Last week’s range was 1.3 to 1.6.  So it’s possible, for instance, that last week it was 1.3 and this week it is 1.5, i.e. it could actually have gone up.

“Second point, which is more important: Let’s suppose we actually knew that R had gone down, let’s say to 1.2, right at the bottom of this week’s range.  If R is above 1, that means that (on average) every infected person infects more than one other person.  If R is 1.2, that means that every 10 infected people are going to infect, on average, 12 people.  So if there are 10,000 infected people this week, there will be 12,000 infected next week.  Any R number above 1 means that (on average at least) the number of infections are increasing.

How could the R number be stable even if infections are rising?

“Same answer the other way round, really.  If R is stable but above 1, infections will rise.  Infections will only stop rising when R goes below 1.  That’s why politicians (and others) keep going on about the need to get R below 1.  It isn’t because ‘below 1’ is a nice low level, it’s because, if R is bigger than 1, infections go up, if R is less than 1, infections go down.”


Prof Kevin McConway, Emeritus Professor of Applied Statistics, The Open University, said:

“The latest estimates of the UK’s R number and growth rate, from SAGE and the Government Office for Science (GOS), have been published.  As always they don’t give a single figure, but instead give ranges within which they think it’s likely that each of the numbers will fall.

“This week’s range for R is from 1.2 to 1.5, meaning that (on average) 10 infected people in the UK will infected between 12 and 15 others.  That obviously means that infections would increase, which isn’t good news.  However, the range is a little lower than last week, when it was 1.3 to 1.6.  While this looks like good news – albeit not particularly good because the range hasn’t changed much and R is still above 1 – we’ve got to be very careful in interpreting it.  It does not mean that R has definitely gone down.  Indeed the ranges include the possibility that R might even have gone up – it could have been 1.3 last week and 1.4 this week, for example.  But at least it allows the possibility of a move in the right direction.

“This week’s range for the growth rate in infections is +4% to +9% per day.  That’s very little changed from last week, when it was +5% to +9% per day, so it allows the possibility that the growth rate might have fallen slightly, but we can’t be sure.  A 4% growth rate would mean that the number of cases doubles in about 18 days, while 9% would mean a doubling in 8 days.  Even a doubling in 18 days is quite a fast rate of increase, it has to be said.

“Today’s preprint from the REACT-1 study also produced estimates of R and the growth rate, based on their swab tests on a representative sample of the English population taken between 18 September and 5 October.  They gave central estimates for R and the growth rate, but probably the most appropriate thing to compare with the SAGE/GOS estimates is the REACT-1 ‘credible intervals’.  These give ranges for R and the growth rate that are consistent with their data, allowing for the fact that it’s a sample and not everyone in the country was tested, so there’s some statistical uncertainty.  The REACT-1 range for R runs from 1.05 to 1.27, so that’s somewhat lower that this week’s SAGE/GOS range for England (1.2 to 1.5, as for the whole UK) – though the ranges do overlap so the two sets of estimates are not actually inconsistent with one another.  The REACT-1 range for the daily growth rate runs from +0.8% to +4.0%, again somewhat lower than SAGE/GOS (a range of +4% to +8% for England), and indeed not quite overlapping.  On doubling time, REACT-1 gives a range from 17 days to 84 days – very wide, but again indicating rather slower growth than SAGE/GOS.

“One important possible reason for the differences is that the estimates from SAGE and GOS use a much wider set of sources of data that REACT-1, which bases its estimates entirely on the rate at which the daily numbers of positive swab tests was growing during the latest round of its survey.  The SAGE/GOS estimates also use data from other sources, for example on hospital admissions and deaths.  This allows more sophisticated models to be used.  However, it also means that some of the data lag behind the current position – for instance, it would take some time after a person is infected before they might have to go to hospital, and longer till their death, if, sadly, that happens.  Therefore the SAGE/GOS estimates may not yet reflect recent changes that affect the transmission rate.  Since the REACT-1 estimates are based on data going right up to only 4 days ago, it’s possible that they are more up to date with the current position – but they may be less reliable because they are based on only one source of data.  It’s good that we are getting estimates from different sources, though it does emphasise the inescapable uncertainties involved.”

All our previous output on this subject can be seen at this weblink:


Declared interests

Prof Kevin McConway: “I am a Trustee of the SMC and a member of the Advisory Committee, but my quote above is in my capacity as a professional statistician.”

None others received.

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