Was lockdown too late?

I've shown elsewhere that the first lockdown did not work. Infections were declining; the peak of infections had passed and the lockdown was therefore not necessary to suppress them. Would lockdown have worked if it had been imposed sooner? With the information available at the time would it have made sense to order a curfew or other non-pharmaceutical intervention (such as selective or general border closures, mask mandates, 'health passports' etc) earlier, and if so, when?

We're all too familiar with the above chart. It's the daily death count by date of death of the first wave of Covid in England and Wales where Covid was mentioned as a cause of death on the death certificate. The day marked orange is when the first curfew (lockdown) was announced. We know what it looks like now, but what did it look like in the early days of the epidemic?

It looks scary. A chart of daily death count from the beginning of March to the lockdown announcement looks a bit like an exponential curve. It's not actually exponential, of course - epidemics never are.

Just how fast was this really changing? A common method to assess how fast something is changing is to measure differences over time. So to assess speed we measure difference in distance from the start point over duration (eg, metres per second, or miles per hour). We measure acceleration as a difference (increase) in speed over time (eg zero to 60mph in 10sec, or 10 metres per second per second (that last one is 1G or the acceleration of a falling object on Earth)). To measure the speed of spread of an epidemic we might want to measure how many more people are infected each day (difference in infections per day). However, we can never acheive this unless we can reliably test everyone each day (we didn't have a rapid Covid test generally available in the UK until December 2020, and there are questions over its sensitivity); we need a surrogate measure - something we can measure which is directly related to what we want to know. Instead we might measure the difference in daily death count each day (eg, how many more deaths on a given day divided by the number of deaths the day before to give a percentage increase for each day) and use this to retrospectively indicate the spread of infections some time before. Using this approach we can calculate that Covid deaths on 23 Mar 2020 were about 12% higher than the day before (197 deaths on 23 Mar 2020, 176 deaths on 22 Mar 2020, (197-176)/176 = 11.9% change) and so on for each day (a true exponential would have a fixed percentage change for each day eg 'each day is 12% more than the previous day').

The number of deaths is increasing each day, but certainly not by a fixed percentage, and the amount it's increasing by seems to be getting less over time. If this continues then we'll reach some point when the change is negative ie when there are fewer deaths than the day before.

• The first day on which we had more than one death was 5 Mar 2020 (2 deaths), but we had reports of a build up of patients in hospitals and we knew that worse was to come.
• For 5 Mar 2020 we had 2 deaths, an increase of 1 from the previous day's count of 1: the daily change was 100%.
• For 9 Mar 2020 we had 5 deaths, an increase of 3 from the previous day's count of 2: the daily change was 150%.
• For 8 Mar 2020 we had 2 deaths, an increase of 2 over the previous day's count of 0: the daily change was infinite (mathematically an infinite increase could be due to 1 more death than zero or everyone in the country - infinite is meaningless in this context).
• For 10 Mar 2020 we had 3 deaths, a decrease of 2 from the previous day's count of 5: the daily change was -40%.

We have a problem here: an infinite increase is meaningless - it gives us no useful information. This sort of problem often occurs when analysing data with very low counts (the data is 'spiky'), very small changes show as very large effects. There's another problem: if a victim dies just before or just after midnight the date of death can be a matter of chance; with very low death counts at the beginning of an epidemic this can result in zero deaths being recorded for a day and that will result in an 'infinity' in the calculations.

One well known method to smooth out spiky data is to use a 3-day (or more) centred average... But what would that do to the larger scale picture?

No, no significant difference in the large-scale picture.

That's better. We've got rid of the pesky infinities. We had better compare the smoothed data with reality for 1 March to the lockdown date to see if we've changed the small scale picture.

The only significant change to the picture is that the 'best fit' exponential looks even less likely to be true.

Since we know it's not exponential (not increasing by a consistent amount each day) we should now look to see how the percentage changes to the 3-day average are changing over time and if there's a trend to that change.

Well look at that: There is a trend - and its a reducing trend. Because we're measuring percentage change in daily deaths, when/if the changes fall to 0% we will have reached a peak in death rate. The trend in 3-day centred average Covid diagosed death data from March to lockdown predicted (using this straight line method) that the peak would occur on 6 Apr 2020. With the benefit of hindsight we know that it didn't; the peak was on 8 Apr 2020, but that's impressively close.

Think about it: the trend in death data before lockdown correctly showed that the peak in deaths would occur in early April. This means the trend in infections leading to the peak and subsequent decline in deaths was already set well before the lockdown announcement. In order to reduce or delay the peak in deaths, some of those infections would have to be prevented or delayed.

So when did the infections which lead to peak deaths occur? If we wanted to reduce or delay those, when should we have intervened - and in what way?

There's a hint in the data that the average lead time between infection and death for those who died was 27 days (about 4 weeks). The peak of deaths was on 8 Apr 2020. Therefore the peak of infections was probably around 12 Mar 2020. If a curfew was to be effective, it would have to have been imposed before that date. By 12 Mar there had been 26 Covid deaths in GB (all of them in England) but only 3 had been registered by then.

'Report 9'

In very early March the UK government was already in thrall to the advice emanating from Imperial College London. It seems the government were being selective about what advice they were listening to.

'Report 9', the Imperial College London paper famous for forecasting half a million deaths, was published on 16 Mar 2020 (4 days after the above estimated peak in infections). The 'Results' section (page 6) opens with this paragraph:

• The first sentence starts with this caveat: 'In the (unlikely) absence of any control measures or spontaneous changes in individual behaviour...'. In 2007 the lead author of 'Report 9' was a co-author in PNAS: The effect of public health measures on the 1918 influenza pandemic in U.S. cities which includes this statement: 'Our analysis also suggests that individuals reactively reduced their contact rates in response to high levels of mortality during the pandemic' - in other words they found 'spontaneous changes in individual behaviour'. The absence of such behaviour was not only 'unlikely', the author had previously shown that such changes in behaviour should be expected.
• It's is clear that the 'control measures' envisaged in the report did not include the then government recommended regular and comprehensive (20 sec) hand washing and avoiding meeting people if we or they felt unwell. Clearly, these must have been considered to be an 'absence of control measures' or the above paragraph renders the rest of the report meaningless.
• In their 'Figure 1A' the peak death rate for 'GB' is shown in late May (say about 22 May 2020) which suggests that the start date for the '3 months' mentioned in the above paragraph is late February or the beginning of March, not the publication date. This is also consistent with the start of the x-axis in the figure at Mar 2020. The actual peak occurred on 8 Apr 2020 not in late May - 44 days (a bit more than 6 weeks) earlier.
• The figure shows the curve for 'GB' reaching a peak of about 22 deaths per day per 100,000 people. The population of England, Wales and Scotland (GB, the island of Great Britain) in 2020 was about 65.86m so their peak represents about 14,340 deaths per day. The actual peak was 1,450 deaths on 8 Apr 2020; a huge number but only just over one tenth of the prediction in 'Report 9'.
• They predict a GB total death count of 510,000. The actual death count (where Covid was mentioned as a cause of death) for the first wave, to 31 Aug 2020, was 56,948 - lower by a factor of 9.
• The curves shown in the figure seem almost symmetrical - this is not just an aesthetic criticism. Epidemic curves usually show a long tail off in comparison with a rapid start (ie a Gompertz curve); the actual death counts do show this effect (see the chart at the top of the page). The curves shown in 'Report 9' seem to be Logistic curves rather than Gompertz curves.



• With a predicted peak on 22 May of 14,340 deaths per day and a total of 510,000 deaths the Imperial College team have defined the shape of the daily deaths curve. An epidemic curve can be tall and narrow or low and wide and still represent the same number of deaths when you add up each day's toll (think of it a bit like the area of a triangle, tall and thin or low and wide). By defining the height (14,340) and the area (510,000) they've effectively defined the width (duration). By setting the date of the peak they've also effectively set the date of the first few deaths (the bottom left corner). We can find the Gompertz curve which matches these parameters.



• The closest match (yellow) seems to be a curve which should show the first epidemic deaths (ie not deaths of visitors who have brought the infection with them) on 18 Apr 2020 (34 days before the peak). However, the first deaths were actually already occurring before 'Report 9' was published in mid-March.
• To be fair the report authors do state 'Epidemic timings are approximate given the limitations of surveillance data'. This suggests that the best fit curve should be shifted earlier (left) on the chart as necessary so that the first predicted deaths coincide with the observed start in epidemic deaths (2 Mar 2020). This gives the formula <cumulative_deaths> = 510,000 * EXP( -15 * EXP( -0.07645 * <dayno> )), where <dayno> = 1 is 1 Mar 2020.
• If we do shift the re-calculated 'Report 9' deaths curve left what would the first 23 days look like as compared with reality?



• A very poor match indeed. By the date of publication of the report (16 Mar) the shifted best fit curve predicted that 5,938 deaths should have occurred; the reality was 153 - nearly a factor of 40 lower. The authors of 'Report 9' (and the UK Government) should have been able to tell from the very earliest death data that the predictions in 'Report 9' were wildly inaccurate (or that the control measures so far taken had been highly effective).
• If we do shift the re-calculated 'Report 9' curve so that the initial deaths (not the peak) coincide with reality we also shift the predicted peak. It moves from 22 May 2020 to 5 Apr 2020 (a shift of about 7 weeks). That's close to the actual observed peak of 8 Apr 2020, which means they got the interval between first few deaths and the peak approximately right; about 5 weeks.
  • If they got the time interval between the first few deaths and the peak in deaths right (~5 weeks) and set their peak at about 22 May 2020, what did they think would be happening between their start date (1 Mar 2020) and their predicted first few deaths (about 17 Apr 2020); about 7 weeks? Is this their assumed average lead time between infection and death for those who died? To try to be fair, their diagram 1A does show deaths starting in early April - but that in itself is not consistent with a peak of 14,340 deaths per day on 22 May 2020 with a total of 510,000 deaths (to go back to the triangle approximation, it can't be that wide and that tall and have that area).
  • If they were assuming an average 7 week delay between infection and death then as soon as the first deaths started occurring (before publication) they should also have assumed the epidemic had been spreading since mid-January 2020.
  • From that assumption, by the time their report was published the epidemic had been spreading in the UK for about 9 weeks - far too long for any proposed border controls or track and trace to have any effect.
  • The widely assumed origin of the Coronavirus, Wuhan, was locked down on 23 Jan 2020 at which time the Chinese authorities had reported 18 deaths. This was a week after the start of the spread of the epidemic in the UK if 'Report 9' is to be believed.
• Either the authors of 'Report 9' did not believe the epidemic should follow a Gompertz curve (the epidemic did, as epidemics do) or they failed to test their model's prediction against the data that was already available before the publication date. Either way it was completely wrong. 'Report 9' is self-contradictory.



• If, as predicted in 'Report 9', 81% of the population of Great Britain became infected over the course of the epidemic that would be about 53.35m people. If 510,000 of these were to die from Covid then the average infection fatality rate (IFR) would be a little under 1%. An IFR of 1% is in the range quoted for pandemic 'flus. 'Flu is certainly a deadly disease but it is also, for most people, self-diagnosed and self-declared; 'I can't come to work today. I've got the 'flu'.
• The reference to 'R0' in the quoted paragraph is the concept that on average, each infected person will infect a number of other people - and so the virus will continue to spread further. If the R0 is below 1 then the infections will reduce. Assigning a fixed R0 greater than 1 is just a round-about way of saying 'exponential' without sounding quite so stupid.
• Figure 1B from the report shows the predicted number of 'cases' during an unmitigated epidemic - though they have omitted to give any scale to the Y-axis. They have, however, placed the peak of cases in late April which means they predict a lag of a little less than a month between peak of cases and peak of deaths. This is consistent with our retrospective analysis of changes in death rates which calculates 27 days between peak infections and peak deaths. However, it is not clear whether they think peak of cases and peak of infections to be the same thing.
• Note that 'Report 9' predictions specifically exclude any deaths due to the health services being overwhelmed; it excludes extra deaths due to delayed consultations and treatments for any other conditions; it only deals with Covid as the cause of death. The ONS Covid mortality figures are based on what the certifying doctor has put as the cause of death - which is often not a single cause but a short list. If Covid is mentioned anywhere on the list of causes of death then ONS will count it as a 'Covid death'. This is a slightly different approach compared with that of other agencies later in the epidemic which counted a death as a 'Covid death' if a person died within 28 days of a positive Coronavirus test. Neither approach is 'wrong' but I think the ONS approach is more accurate though more subject to delays.
• Despite the obvious severe errors in 'Report 9' at the time of its publication, the lead author was a prominent member of SAGE. However, he briefly fell from grace when he broke the lockdown rules just one week after they were announced.
• On the same day 'Report 9' was published the Prime Minister announced that people "should avoid pubs, clubs, theatres and other such social venues" and "It looks as though we are now approaching the fast growth part of the upward curve". It appears that 'Report 9' had convinced him and his advisers.

At the start of the first lockdown in the UK we were bombarded with the message that we had to 'Stay at home. Protect the NHS. Save lives.' ie take action to make the progress of the epidemic 'low and wide' (as in the example of the three Gompertz curves above) in order to prevent the daily rate of new infections overwhelming the health service (my paraphrasing). However, lockdown could not have averted the majority of infections which led to the peak in deaths on 8 Apr 2020 as most of those victims had been infected in early March.

The straight line trend in changes to death rates from early March to lockdown during the first wave of the epidemic in England and Wales pointed to the peak daily death rate occurring in early April, which is what actually happened. If we assumed the death toll was going to follow a Gompertz curve the data up to 23 Mar 2020 also forecast a peak in early April and a total death count of 36,250 by 31 Aug 2020. About 4 days late with the peak and 30% low on the total - but a lot closer to reality than the insane predictions in 'Report 9'.

By mid-March the trend in death data was already indicating an early April peak. To alter this, any intervention would have to have averted the infections leading to those deaths. In other words, lockdown (if it was effective) would have to have started in mid-February. By mid-February 'Report 9' had not been published and there had been two deaths attributed to Covid in England and Wales; I doubt that Parliament would have granted the Government the curfew powers based on the available evidence.

I'm pleased to say that, unlike in many other states, the UK Government normally has very limited powers to order a curfew. In order to impose 'lockdown' (and all the other changes to tax, benefits, furlough, employment, contact tracing, social distancing, tenancy protection, border controls and infection and death registration and everything else that came with it) the Government had to persuade Parliament to approve the Coronavirus Act 2020 (342 printed pages). This Bill was given its First Reading on 19 Mar 2020 (three days after 'Report 9' was published) and was passed without Division (Parliament did not vote on it, it went through without any MP calling for a vote) and received Royal Assent (became law) on 25 Mar 2020 - though the curfew was actually announced two days before it became law. The Opposition party leader had previously stated that his party would not seek to debate or make any ammendments to the Government's Bill; a source said that "...Labour was attempting to strike a balance between scrutinising government and facing up to the virus". The whole political establishment conspired to approve lockdown.

Lockdown on 23 Mar 2020 could not have affected the peak and subsequent decline in deaths as the infections which led to those deaths had occurred before lockdown. If it did not cause the decline in infections then it was not necessary; some other effect had already done it.

Note that there was, however, a very small (about 3.5%) short-term (for about 5 weeks) improvement in the death rate trend that started at around 19 Apr 2020 (about 11 days after the peak of deaths and about 4 weeks after lockdown) which may have been associated with the lockdown. That improvement was cancelled out over the following 9 weeks. There was no other improvement in the trend that could have been caused by the lockdown.

Much is said about the UK Government failing to heed the warning from what was happening in Italy. The following is from an article on Wikipedia extracted on 3 March 2022:

• Early February: Virus detected in overseas visitors to Italy and a returning traveller.
• Late February: Virus detected in two regions of Italy.
• Early March: Virus detected throughout Italy.

It appears that over a period of only about 3-4 weeks the virus spread throughout Italy. This thing was not going to be stopped by a curfew. Closing borders after it was already spreading within the United Kingdom would have been futile.

There was no warning available from what was happening in Italy until late February by which time the infection was well established in the UK. About two weeks later the infections which led to the peak period deaths in England and Wales were already occurring.

It's important to realise that although this analysis is based on death date and not death registration date, the death date and diagnosis information for each death would not have been available until it was actually registered. Delays in the certifying doctor's paperwork or elsewhere in the registration process would have resulted in delays to the data becoming available. It typically takes 5 days or so for a death to be registered - for example: by the date of publication of 'Report 9' we now know (from ONS publications) that there had been 150 diagnosed Covid deaths in England and Wales but only 16 had completed registration. We should hope that Government advisers and decision makers had access to more up-to-date information than the ONS weekly publications, but faster access to the data before each registration process was complete might well have introduced errors. The Coronavirus Act 2020 included specific measures to try to reduce death registration delays to a minimum.

We've seen what the chart of %change in the 3-day centred average death count from March up to lockdown looked like, and how it trends toward a peak in death rate in early April. But should our decision makers have believed the trend would continue to a peak at around that time? Here's what the same data looked like right up to that peak:

A very good match. Yes, it would have been a useful prediction - what other empirical evidence could they have relied on?

The UK Government should have realised before, or very soon after lockdown that the predictions in 'Report 9' were too high by a factor of ten. There was empirical evidence for this in the first few weeks of Covid death data but the government followed the guidance of epidemic computer modellers instead of the evidence. The Opposition party 'Shadow Cabinet' would have had access to the same data and reports as the Government and yet some called for harder and earlier lockdown - but I guess that's just the way of party politics. With the perspective of hindsight after the first wave and lockdown, why did the Government and Opposition and Regional government leaders push for and support the second and third lockdowns (on 5 Nov 2020 and 6 Jan 2021) when they should have known that the first lockdown had been ineffective and unnecessary?

Finally:

My answer to the question posed in the title of this post should now be obvious: No, lockdown was not too late. It should never have been tried. Having tried it once it should not have been tried the second and third times in the UK.

Many governments throughout the world followed curfew and similar socially and economically destructive policies. Maybe they have evidence that such policies were necessary or effective for their countries. If so, they should present that evidence. If not, their citizens should hold them (including any opposition parties) to account (obviously this can not apply in un-democratic countries).

Exponential:

It was never exponential. Saying or implying it could be or was exponential is foolish fear-mongering.

Key points:

• The Imperial College London 'Report 9' was clearly wrong based on the observable mortality data available before it was published on March 16 2020. The lead author was a prominent (and vocal) member of the Government's Scientific Advisory Group for Emergencies (SAGE).
• By the time of the first lockdown in England and Wales on March 23 2020, the trend in mortality data was pointing to a peak in early April; infections had already peaked and were declining by that time.
• All political parties were complicit in implementing the lockdown policy in the UK. The Coronavirus Act was passed by the House of Commons and House of Lords without Division - and given immediate Consent by the Scottish Parliament.
• With clear evidence available that the first lockdown in the UK was neither effective nor necessary it is very disappointing that the second and third lockdowns were implemented.

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.