COVID-19 Case data (UK)

 COVID-19 Case data (UK): May - September.

    I seem to be among the very few commentators who present data in semi-logarithmic plots. My rationale is that the chance of catching the virus depends on the fraction of the population carrying active viruses. So the rate of increase of infection depends on the level of infection in the population. This is the characteristic of logarithmic growth; as in the growth of bacteria in fresh medium, and in the cooling of a jug of hot water, where the rate of loss of heat depends on the temperature difference between the jug and the room air. 

    The advantage of semi-logarithmic plots is that, in a steady situation, with the virus spreading at a steady rate and data points following a continuously steepening upward curve, it is hard to extrapolate -- i.e. to predict. But, when plotted as their logarithm (against time on the x-axis) the points will follow a straight line, and extrapolations (i.e. predictions) can be made, trends can be determined, and changes in regime detected.

    In the picture below, I present log(base10) of the daily increment of new cases (as reported by the government) on the vertical axis against the days since 30th April 2020 on the horizontal axis. (1,000 cases daily shows as 3.0; 10,000 would show as 4.0; 1st June shows as 32, etc.)

    The falling line of blue data points shows that during lockdown the virus was being steadily eliminated from the population, monotonically, and steadily. In epidemiological language R0 < 1.0. The R^2 value of 0.934 indicates that the data conform rather well to a straight line (with the slope of -0.0152 per day).

    The rising line of pink data points shows that after the relaxation of lockdown the virus has been gaining ground in the country with a rather consistent, quasi-monotonic, rate. I.e. between 9th July (day 70) and 4th September (day 127), the R0 value has been greater than 1.0. Not "between 0.9 and 1.1", nor "levelling off", as reported by the BBC on many occasions during that period; it was consistently greater than 1.0 all that time. How the BBC could continue through July and August saying the viral spreading rate was below 1.0 baffles me. 

    On 5th September there was a jump in the daily increment that was large enough for everyone to notice (See the last 3 data points in pink). It is impossible for me to fit a line to 3 points, so we shall have to wait a week to see if a new regime is in operation – a new slope on the semi-logarithmic plot. A 'back to work/school' regime.

(See also previous blog-posts.)