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

The government have published the latest estimates for the COVID-19 R number and growth rates.


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

“The government’s own estimates that the infections double about every seven days suggest that the actual R number now is higher than the one published today. The R number is based on the data from some weeks ago, which include hospitalisations and death rates. Since the infections a few weeks ago were mainly spreading among younger people, low hospitalisation and death rates have most likely played a role in R being estimated to be on the lower side. Since the R number also depends on the number of positive tests,  and testing capacity has been reached, combined with delays in getting the test results, this further suggests that the true R number is higher than today’s estimate. The number of hospital admissions and hospital diagnoses in England has risen from 80-90 people in the beginning of September to almost 270 individuals by the 22nd September, and this steady increase in hospital admissions combined with the rising R number suggests that the situation is becoming much more critical.”


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

This comment also refers to the ONS data rounded up on here

“The latest data show that the infection is currently growing exponentially in all regions of England, and of the UK as a whole. Whereas there are some differences between regions in terms of the proportion of population testing positive, there appears to be very little difference in rates of growth, suggesting that it is no longer possible to consider the situation from the perspective of just individual hotspots driving the overall trend, but rather all regions are already experiencing growth in cases. ONS data indicate that in a two-week period from the 7th to 19th September the percentage of positive tests in England has more than doubled, and with roughly the same number of tests being performed, this adds further evidence of significant rate of growth of infection. Moreover, the evidence indicates that the rates of infection have increased across all age groups, which, in light of what is known about this disease, indicates a potential danger of increasing hospitalisations once the infection targets larger numbers of older people.”


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

“This week’s updating of the estimates of the R number and the growth rate of the COVID-19 pandemic, from SAGE and the Government Office for Science (GOS), has been published. The ranges of values for both of these numbers for the UK are a little higher than they were last week. They are estimating R as between 1.2 and 1.5 (last week’s estimate was 1.1-1.4), and the daily growth rate in new infections as between +4% and +8% (last week the estimate was +2% to +7%). These numbers leave no serious doubt that infections are increasing, in the opinion of SAGE and the GOS, and that increase appears to be happening across the whole country. The estimates for the different regions of England are now all pointing to growing numbers of cases. The same is true for England as a whole, and also for the (separately published) figures for Scotland and Northern Ireland. The position is a bit less clear for Wales, though the group advising the Welsh government certainly believes that the epidemic is increasing there as well. The position gives considerable cause for concern, and I hope that the recent changes in restrictions on what we can all do will slow and eventually reverse this increase.

“It’s not surprising, given other data, that the ranges are higher this week than last. That may not, however, represent a true increase in the R number or the growth rate between last week and this. These estimates are based on several different sources of data. For some of those sources, particularly numbers of hospital admissions, ICU admissions, and deaths, the patterns of increase or decrease are delayed compared to changes in new infections, because it takes time after someone has been infected before they may need hospital treatment or, sadly, die from their infection. So the current R and growth rate estimates will not have fully taken changes in those figures into account.

“The growth rate range (for the UK) of +4% to +8% indicates that GOS and SAGE estimate that the number of new cases is increasing by between 4% and 8% per day. A 4% daily growth rate corresponds to a 32% weekly growth rate (a bit more than 7 x 4 because each day’s increase is a percentage of the previous day’s already increased figure – a bit like compound interest).  And it corresponds to a time of about 18 days for the number of infections to double. An 8% daily growth rate corresponds to a weekly growth rate of about 71%, and a doubling time of about 9 days, just a bit over a week. So, in very broad terms, these growth rates do match the conclusions on the growth of new cases in today’s update on the ONS infection survey. And they are certainly big enough to be worrying.”


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


Declared interests

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

None others received.

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