This is an extract from the Government daily Coronavirus briefing on 2nd April 2020, led by Matt Hancock, with Professor Stephen Powis, Medical Director of the NHS in England.
In this clip, Prof. Powis states that he thinks there is “early academic evidence” that the R0 “Reproduction Number”, (what he calls the transmission rate) reflecting the average number of people infected by one person, “may have fallen below 1”. This is an important target, because when R0 for a given epidemic is below 1, the epidemic will die out.
My issue here is that I would like to see the evidence.
In Matt Hancock’s statement, he said that “the best scientific analysis is that” the “doubling” period for the rate of infection of the virus (another important statistic, used by Johns Hopkins University in many of their charts for the epidemic) was between three and four days.
In the early stages of a rapidly growing epidemic, either of three or four days lead to quite different outcomes (for power series (or exponential) growth) after, say, 30 days (since day zero, defined as 100 cases), for the total number of people infected – 3 days leads to 100,000 cases, and 4 days to 18,000.
See my previously posted spreadsheet to run your own numbers for this:
https://docs.google.com/spreadsheets/d/1kE_pNRlVaFBeY5DxknPgeK5wmXNeBuyslizpvJmoQDY/edit?usp=sharing
My opinion is that it’s an optimistic range, but in any case it is too wide to be meaningful without more detail. I suspect 2.5 days (which would lead to 400,000 cases) might be a better number, but without seeing the scientific data – the “evidence” in either case – who knows?
But do you see how sensitive outcomes are to quite small changes in estimates to the input data at this early stage in the epidemic?
Both of these video statements sound to me to be too optimistic, and smack of concern to reassure the public rather than undiluted science.
My mention of “exponential” above reminds me to repeat my usual issue with presentations of log scale graphs without explanation.
The visual appearance of this chart from the 2nd April update, to the average member of the public, doesn’t really highlight visually that the growth in numbers is exponential – it looks more as if the rates are flattening. It requires scrutiny of the y-axis to see that the top gridline in the chart is representing a number (10,000) 200 times higher than the baseline, 50. It’s at least careless not to mention that, other than “Logarithmic scale” (not saying whether x- or y-axis) in a tiny font at the bottom of the chart. A similar chart was shown on 3rd April too.
I’m guessing that the chart above was drawn straight from either the Worldometer, or Johns Hopkins University site without due consideration of its meaning for non-practitioners.
They do know the difference, of course; this DHSC chart, with linear axes, was also presented, and it does show the characteristic exponential growth of the epidemic, in this case for the deaths from the outbreak.
