Did the England and Wales second and third lockdowns work?

You can find an analysis of the first lockdown in the previous post

The above chart of deaths attributed to Covid-19 is derived from ONS weekly deaths data up to week 34 of 2021 published 14 Sep 2021.

• The deaths data is drawn from the 'Covid-19 - Daily occurrences' tab of the above spreadsheet.
• Within that spreadsheet tab I have selected the column headed 'England and Wales'.
• The cumulative deaths data is simply a running total of the daily deaths.
• There is a remarkable similarity in the peaks covering Mar-2020 to Aug-2020 and Dec-2020 to Jun-2021 - but with an added 'bump' before the latter.

Let's zoom in a bit closer and concentrate on 22 Aug 2020 to 11 Jun 2021.

The dates of the second and third lockdowns have been highlighted.

If you squint a bit, the cumulative deaths curve (green, scale to the right) looks a bit like two Gompertz curves with a bit of an overlap in the middle.

Let's not worry about what that might mean at this stage, let's just see if we can find two Gompertz curves which match the data.

Yes we can: The calculated combination curve has the formula:

Gompertz-1 + Gompertz-2

where
Gompertz-1 = 4.42E+04 * exp(-1.47E+01 * exp(-2.77E-02 * dayno))
Gompertz-2 = 4.43E+04 * exp(-1.47E+04 * exp(-6.47E-02 * dayno))
and dayno=1 is 22 Aug 2020.

• That's another astonishingly close fit - I know we were looking for the best fit but this is remarkable. We can barely see the reality (green) curve behind the calculated (red) curve.
• The data fits closely to two overlapping epidemic curves.
• Both Gompertz curves (dotted lines) plateau at about 44,000 deaths giving a total of about 88,000 deaths attributed to Covid-19 since September 2020.

If we plot the calculated daily deaths we get this:

Or the same chart stacked with reality superimposed.

Let's plot the differences between the actual cumulative death count and the calculated values (ie find how the calculated value differs from reality).

• We're interested in when the differences curve (blue, right scale) changes direction between rising (bad) and falling (good), and what may have caused the trajectory to change.
• The dates of good and bad changes are labelled (in black); also, policy interventions (in red) and peaks in death rates (in blue).
• From the previous analysis we suspect there may be an average 27-day lag between infection and death (for those who die). The alternative 16-day lag definitely does not show in the data.
• At this point let's tackle the thorny issue of interpretation of the facts.

• First, the 'elephant in the room': Two overlapping Gompertz curves. What could that mean?
  • The answer is simple but raises a few more questions: It's two different epidemics.
  • It's either two different subsets of the England and Wales population that don't mix... or it's two different diseases.
  • Looking at the shape of the two curves, the first is wider and flatter (95% of deaths in 199 days) than the second (95% of deaths in 84 days) it seems reasonable to think these may be caused by two different bugs. Compare these with the first wave in March-September 2020; 95% of deaths in 98 days. Delta seems to behave more like the original bug.
  • The deaths from the first of the two epidemics seem to have started in early September 2020 which coincides with news reports of the so-called 'Kent' variant (properly named Alpha variant).
  • The deaths from the second epidemic seem to have started in mid-December 2020 which coincides with news of the so-called 'Indian' variant (properly named Delta variant).
  • It certainly looks like two distinct epidemics overlapping which also suggests that catching one variant does not confer immunity to the other - which is a worrying thought.
• It's tempting to try to analyse the two epidemics separately but I don't think that can work; If lockdowns reduce the number of infections or slow down the rate of increase then they should affect both epidemics.
• However, it's quite possible that the two different diseases have different 'lags' between infection and death (for those that die) which will complicate the analysis. For example, according to the calculated curve, on 16 Jan 2021 82% of the deaths were due to Delta variant and 18% due to Alpha - so the death rate on that day potentially relates to two different infection rates on different dates and two different infection fatality rates.
• There seem to be five points of interest (3 good, 2 bad):
  • 7 Oct 2020 (good): A fairly slow change.
  • 9 Dec 2020 (bad): A sharp change for the worse.
  • 31 Dec 2020 (good): A very sharp change for the better.
  • 15 Jan 2021 (bad): Another sharp change for the worse.
  • 25 Feb 2021 (good): A slow change.
• However, bear in mind that the observed changes only amount to +1.4% (bad) to -0.7% (good) of the overall calculated and observed death toll.
• In addition we have two major policy changes which were intended to improve matters:
  • 5 Nov 2020: Second lockdown.
  • 6 Jan 2021: Third lockdown.
• If the second lockdown (5 Nov 2020) had a beneficial effect on the infection rate and the subsequent improvement in death rate (31 Dec 2020) then the average lag between infection and death is 56 days.
• If the third lockdown (6 Jan 2020) is associated with the following improvement in death rate (25 Feb 2021) then the average lag is 50 days.
• Alternatively, if the second lockdown (5 Nov 2020) and the subsequent deterioration (9 Dec 2020) are associated then the effect took 34 days to manifest.
• If the third lockdown (6 Jan 2020) and the subsequent deterioration (15 Jan 2021) are associated then the effect took only 9 days to manifest.
• There are no clear associations (good or bad) between the dates of the lockdowns and changes to the trajectory of the cumulative death curve relative to the sum of the two natural epidemic curves.

The second and third lockdowns in England and Wales did not work.

If you wish to comment you may email me at: SoundOfReason0 at gmail dot com. If I append your comment I will not publish your email address.

The first, second and third lockdowns in England and Wales did not work.

Since June 2021 there has been a slow increase in deaths attributed to Covid-19. Will our leaders be panicked into imposing another lockdown? If they do, is it more or less likely to work than the first three?

I see no reason why lockdowns might have worked elsewhere in the world but not in England and Wales. If you have access to data for other countries or regions and can prove that lockdown as a policy worked to limit sickness and deaths or to prevent healthcare being overwhelmed then please publish your analysis. Please don't bother quoting official figures from China; nobody believes them.