Modelling

The Modellers Keep On Making the Same Errors – And the Implications Are Huge

There follows a guest post from our in-house doctor, formerly a senior medic in the NHS, who draws attention to the errors made repeatedly by the modellers and government advisors and the huge implications of them.

Napoleon Bonaparte remarked that “history is the version of past events that people have decided to agree on”. When the official version of the pandemic is written, I wonder what analysis will be made of the role of statistical modellers and public health experts in driving Government policy over the last 18 months?

To inform this question it may be helpful to examine the recent evidence of how predictions have matched up to real events. For example, on September 8th, SPI-M-O (one of the multitudinous acronym salad bodies advising the Government), produced a paper entitled “Medium-term projections“.

Perhaps mindful of the woeful inaccuracy of previous predictions, the very first sentence heavily caveats the entire document:

These projections are not forecasts or predictions. They represent a scenario in which the trajectory of the epidemic continues to follow the trends that were seen in the data up to September 6th.

If that is the level of confidence the authors of the report have in their own abilities, one rather wonders what value this publication contains – yet this is the level of advice being given to decision-makers.

Firstly, to the “projection” of admissions. The document is in PDF format, so I am unable to reproduce it here, but the graphical representations show a 90% confidence interval fan chart for the period September 12th-28th. Hospital admissions in England are “projected” to be between 600 to 1,200 per day – a fairly wide spread. Graph One shows what actually happened – daily admissions on the blue bars, seven-day moving averages on the brown line.

It is clear that admissions have been consistently below the lower ‘projection’ for the entire period and the seven-day moving average at the end of the month was below 500 admissions per day.

Nailed It! Daily Sceptic Accurately Predicts the Delta Surge in Seven Countries

Two months ago Anthony Brookes, Professor of Genomics and Health Data Science at the University of Leicester, wrote an important piece for the Daily Sceptic in which he assembled the “Covid jigsaw pieces into a complete pandemic picture”.

To recap, this was his summary of his argument:

  • A series of SARS-CoV-2 variants have arisen, many of which possessed a transient selective advantage that led to a wave of infection that peaked some three-to-four months later. Several such variants have spread globally, though different successful variants have arisen simultaneously in a number of countries. The result is a three-to-four month wave pattern per country, which is also apparent globally.
  • Seasonality affects variant transmissibility. Colder seasons accelerate the growth and increase the size of waves, but the continually changing environment may also differentially affect the relative transmissibility of competing variants (i.e., negatively as well as positively), thereby helping to terminate previously dominant variants and promote the growth of new ones. 
  • Overall there is a minimal positive impact from quarantine policy, isolation requirements, Test and Trace regimes, social distancing, masking or other non-pharmaceutical interventions. Initially, these were the only tools in the tool-box of interventionist politicians and scientists. At best they slightly delayed the inevitable, but they also caused considerable collateral harms.  
  • Immunity created by SARS-CoV-2 infection, layered on top of pre-existing immunity due to cross-immunity to other coronaviruses, provides good protection against infection, severe disease/death, and being infectious. Immunity created by vaccination also helps protect against serious disease and death, but does little or nothing to provide protection against infection or being infectious (which completely negates the case for vaccine ID cards). 
  • Population immunity stems mainly from natural infections, with vaccines adding only slightly to this (and only in recent months). Population immunity is created by societal waves of infection and is somewhat variant-specific. An emerging new variant is able to infect (or re-infect) some fraction of individuals and this serves to top up and broaden the scope of our population immunity to also protect against the new variant. 
  • This empirical and data-driven understanding of the pandemic allows us to make predictions. Such predictions don’t look good for some of the U.K.’s new Green List countries. But in these and all other places the ongoing arms-race between viral mutations and growing human immunity will always eventually be won by the human immune system. The virus then becomes a low-level endemic pathogen in equilibrium with its human host species. If this were not the case all humans would have been wiped out by viruses eons ago!

In the piece he made some very specific predictions about what would happen over the following months, and we’re now in a position to see how close he got to the target. He wrote:

With an essentially complete Covid jigsaw picture now assembled using an empirical data-driven approach, we can offer up some testable predictions. The first is that current Delta waves unfolding in different countries will reach natural peaks around three-to-four months after this variant arrived in each location. For example, considering countries recently added to the U.K.’s Green List, we would expect: Slovenia, Slovakia and Romania (where Delta arrived little more than one month ago) will see their nascent summer waves grow further and peak in about two months’ time; Latvia (where Delta has only just arrived) will face a multi-month wave starting very soon; and Austria, Germany and Norway (where Delta has already been present for several months) will likely see their summer waves peak around the end of August. NPIs will do little to change this, and neither will vaccines (see Israel for evidence of this).

So the specific predictions were:

  • Reported cases in Slovenia, Slovakia and Romania peaking around about now.
  • Latvia to currently be on the up-slope.
  • Germany, Austria and Norway to peak around the end of August.

Let’s have a look.

India Confounds the Modellers

What happened to India’s summer and autumn waves? After suffering a large surge with the emergent Indian variant (i.e., Delta) in the spring, India has defied modellers’ predictions by remaining very quiet since.

In August, Rajib Dasgupta, Chair of the Centre of Social Medicine and Community Health at Jawaharlal Nehru University, wrote for the Conversation about the “likely” imminent new autumn surge.

With about 40,000 cases and 400 deaths each day as of mid August, a new uptick is likely in the cards. The Indian states experiencing most of these new cases are those with relatively lower sero-prevalence, ranging between 50% and 70%. The 400 million sero-negative pool – that is people who have not been infected or had the vaccine – continues to be a large vulnerable group.

Forecasting by modellers indicates a third wave beginning in August and peaking at 100,000 to 150,000 infections a day by October. An alternative projection expects the peak in cases going until November.

It’s October now and the reality, of course, is a low level of infections since June and no new surge throughout summer and autumn so far. Below is the graph showing the predictions from the modelling of Mathukumalli Vidyasagar and Manindra Agrawal of the Indian Institute of Technology that Rajib Dasgupta cites above. I have added in the line of actual ‘cases’, which shows that they have trended well below the ‘optimistic’ scenario since the moment the prediction was made.

The Government’s Latest Scary Modelling is Already Wrong

There follows a guest post by Daily Sceptic reader Graham Williams (a pseudonym), a maths graduate and by profession an analyser of business plans, models, forecasts and funding requests. He is not impressed with the latest Government pandemic modelling.

I have just read the SPI-M consensus statement paper of September 8th, which appears to be at the heart of the recent stories about possible future lockdowns etc. This paper seems to be as big a load of negative, hyperbolic scaremongering as all the ones they have issued so far this year (February at the start of the roadmap, March, April, June and July).

In paragraph two they state: “SPI-M-O groups have reflected on their modelling of Step 4 of the Roadmap, and despite unexpected falls in cases in mid-July 2021, these scenarios can still be used to consider the future autumn and winter trajectory.”

They appear however not to have reflected that were it not for the unforecast Delta variant their modelling since February would have overstated the position of deaths, cases, and hospitalisations by June 21st by around 1,000%. Even with the rise caused by the variant, their forecasts remained hugely overblown, but they still continue to model with the same flawed methodology.

After paragraph two there follow about 18 paragraphs of largely unsubstantiated waffle with a few facts thrown in.

One of the facts is that R is currently (i.e., at the date of the paper) between 0.9 and 1.1, so broadly flat. The covering page to the report says: “These are not forecasts or predictions… They are based only on the observable trends and data available at the time the projections were produced.”

Had the modelling actually done what it said on the tin, project observable trends, then it would have been in line with their own medium-term projection of September 8th, which shows a fairly flat trend for September, even if arguably the base they have used is a bit low.

The Latest Paper From Neil Ferguson et al. Defending the Lockdown Policy is Out of Date, Inaccurate and Misleading

Neil Ferguson’s team at Imperial College London (ICL) has released a new paper, published in Nature, claiming that if Sweden had adopted U.K. or Danish lockdown policies its Covid mortality would have halved. Although we have reviewed many epidemiological papers on this site, and especially from this particular team, let us go unto the breach once more and see what we find. The primary author on this new paper is Swapnil Mishra.

The paper’s first sentence is this:

The U.K. and Sweden have among the worst per-capita Covid mortality in Europe.

No citation is provided for this claim. The paper was submitted to Nature on March 31st, 2021. If we review a map of cumulative deaths per million on the received date then this opening statement looks very odd indeed:

Sweden (with a cumulative total of 1,333 deaths/million) is by no means “among the worst in Europe” and indeed many European countries have higher totals. This is easier to see using a graph of cumulative results:

But that was in March, when the paper was submitted. We’re reviewing it in August because that’s when it was published. Over the duration of the journal’s review period this statement – already wrong at the start – became progressively more and more incorrect:

The Figures Don’t Match Up To the Fear, a Doctor Writes

There follows a guest post from our in-house doctor, formerly a senior medic in the NHS, who says the widely trailed tsunami of hospitalisations has not only failed to arrive after ‘Freedom Day’, but we seem to be on the downslope of the ‘third wave’.

The philosopher Soren Kierkegaard once remarked: “Life can only be understood backwards, but must be lived forwards.” I have been reflecting on that comment, now we are three weeks since the inappropriately named July 19th ‘Freedom Day’. Readers will remember the cacophony of shrieking from assorted ‘health experts’ prophesying certain doom and a tidal wave of acute Covid admissions that would overwhelm our beleaguered NHS within a fortnight. Representatives from the World Health Organisation described the approach as “epidemiologically stupid”. A letter signed by 1,200 self-defined experts was published in the Lancet predicting imminent catastrophe.

Accordingly, this week I thought I should take a look at how the apocalypse is developing and then make some general observations on the centrality of trust and honesty in medical matters.

Let’s start with daily admissions to hospitals from the community in Graph One. Daily totals on the blue bars, seven-day rolling average on the orange line. Surprisingly the numbers are lower than on July 19th. How can that be?

Perhaps there are more patients stacking up in hospitals – sicker patients tend to stay longer and are hard to discharge, so the overall numbers can build up rather quickly. So, Graph Two shows Covid inpatients up to August 5th. Readers should note that Graph Two includes patients suffering from acute Covid (about 75% of the total) plus patients in hospital for non-Covid related illness, but testing positive for Covid (the remaining 25%). How strange – numbers seem to be falling, not rising. This does not fit with the hypothesis – what might explain this anomalous finding?

Maybe the numbers of patients in ICU might be on the increase – after all, both the Beta variant and the Delta variant were said to be both more transmissible and more deadly than the Alpha variant. Graph Three shows patients in ICU in English Hospitals up to August 5th. It shows a similar pattern to Graph Two – a small fall in overall patient numbers in the last two weeks. I looked into the Intensive Care National Audit and Research Centre ICU audit report up to July 30th. This confirms the overall impression from the top line figures. Older patients do not seem to be getting ill with Covid. Over half the admissions to ICU with Covid have body mass indices over 30. Severe illness is heavily skewed to patients with co-morbidities and the unvaccinated. Generally speaking, the patients have slightly less severe illness, shorter stays and lower mortality so far.

Finally, we look at Covid related deaths since January 1st, 2021, in Graph Four. A barely discernable increase since the beginning of April.

So, whatever is going on with respect to the progress of the pandemic, the widely trailed tsunami of hospitalisations has not arrived yet – in fact, we seem to be on the downslope of the ‘third wave’.

What the Modellers Still Don’t Understand About Herd Immunity

Bristol’s Professor Philip Thomas has a new piece in the Spectator this week. Readers may recall that I criticised his previous pieces for what seemed in my view to be wildly over-the-top predictions of the likely scale of the Delta surge.

In June, he predicted “an enormous final wave“, in which the virus “would quickly seek out the one-in-three Britons who are still susceptible: mainly the not-yet-vaccinated” and peak in the middle of July (the bit he got right) “at anywhere between two million and four million active infections“. According to the ONS, around 951,700 people in the U.K. were PCR positive in the week ending July 24th, and that appears to be the peak, which is less than half of Professor Thomas’s lower estimate.

He now admits: “The situation is better than I bargained for at the beginning of June and also better than my estimates a month later.” In fact, it’s so much better, that he thinks “the decline in active infections can only mean that England is about to reach the herd immunity threshold for the Delta variant”. By which he means that “around 86% of England’s adults and children must now be immune”. On this basis he argues that it is “extremely unlikely” that there will be a new Covid surge in the coming winter.

The problem with this analysis is it is still based on the SAGE assumption that herd immunity is a once-for-all-time thing, that was made harder to reach by the more transmissible Delta variant, but which we have now just achieved, mostly through vaccination, and it will now keep us safe.

An Interview With Philippe Lemoine

Philippe Lemoine is a PhD candidate in philosophy at Cornell University, with a background in computer science. He’s also a blogger, a research fellow at the Centre for the Study of Partisanship and Ideology, and a lockdown sceptic. During the pandemic, he’s written several detailed articles about the efficacy of lockdowns. I interviewed him via email.

On December 4th, you published an article on your blog titled ‘Lockdowns, science and voodoo magic’, which criticised the well-known paper by Flaxman et al. That paper (which has been cited more than 1,300 times) concluded, “major non-pharmaceutical interventions – and lockdowns in particular – have had a large effect on reducing transmission”. Could you briefly summarise your criticisms?

I made two main points against that paper. First, the model assumed that only non-pharmaceutical interventions affected transmission, so any observed reduction in transmission could only be ascribed by the model to non-pharmaceutical interventions. Since in fact transmission went down quickly everywhere during the first wave, the only question was how much of that reduction would the model attribute to each intervention. But the fact that non-pharmaceutical interventions were jointly responsible for the entire reduction in transmission was not something the model inferred from the data, it was assumed at the outset by the authors when they defined the model. A consequence of this fact is that, when they compute a counterfactual scenario in which there weren’t any non-pharmaceutical interventions to estimate how many lives were saved by lockdowns and other restrictions, the authors just assume that cases would have continued to rise until the herd immunity threshold was reached and would only start to go down then. Although the authors did not deem it necessary to reveal this small detail, this meant that, in their counterfactual, more than 95% of the population was already infected by May 3, which is preposterous. Even one year and a half after the beginning of the pandemic, there isn’t a single country where the proportion of the population that has been infected even comes close to such a figure, not even in countries where restrictions were extremely limited. So when the paper finds that non-pharmaceutical interventions in general and lockdowns in particular saved three million lives in Europe alone during the first wave, they only reach that conclusion by comparing the actual number of COVID-19 deaths to the number of deaths in a ridiculous scenario where essentially everyone had been infected. Yet this preposterous estimate was taken seriously by the entire scientific establishment and, as you noted, the paper became one of the most cited studies on the COVID-19 pandemic.

The second point I made is that, not only was this result based on totally unrealistic assumptions, but the authors failed to disclose a key result that completely undermined their conclusion. As I explained above, the model was bound to attribute the entire reduction in transmission that was observed in Europe during the first wave to non-pharmaceutical interventions, the only question was how much of it would be attributed to each intervention. Their headline result was that, apart from lockdowns, nothing else had any clear effect, which meant that lockdowns were responsible for the overwhelming majority of the 3 million lives that, according to this study, non-pharmaceutical interventions had collectively saved. However, Sweden was included in the study and never locked down, yet only a tiny fraction of its population was infected during the first wave. How is that possible if only lockdowns have a substantial effect on transmission? I knew this made no sense, so I downloaded the code of the paper to reproduce their analysis on my computer and take a closer look at the results. Their model allowed the effect of the last intervention, which happened to be a lockdown everywhere except in Sweden, where it was a ban on public events, in each country to vary. What my analysis of their results showed is that, in order to fit the data, the model had to find that banning public events reduced transmission by ~72.2% in Sweden but only by ~1.6% elsewhere. In other words, according to the model, banning public events had somehow been 45 times more effective in Sweden than anywhere else. Now, unless you believe there are magical anti-pandemic fairies in Sweden that somehow made banning public events 45 times more effective than elsewhere, this obviously never happened. Rather, what this means is that the model was garbage, which in turn means that we have no reason to believe the paper’s headline result that lockdown had a huge effect on transmission. There is a lot more in my piece about that paper, which I methodically demolish, but those are the main points.

The SAGE Models are Already Wrong

In a recent article, we considered the implications of the U.K.’s spring rise in infections, given that before now the assumption has been that coronaviruses are seasonal at northern temperate latitudes. Do we have to dismiss that hypothesis in light of the ‘Third Wave’?

Here we argue that, contrary to Government claims, the British summer is indeed finally impacting viral transmission, with sharp falls in positives reported across the U.K. In England, reported cases have more-or-less halved in a week, from 50,955 to 25,434.

This sharp fall runs counter to all three of the most recent SAGE models driving Government policy, which predict rising infections leading to peaks in hospital admissions in high summer – and by implication falsifies the assumptions upon which these models are based.

Parsimony predicts the summer troughs and winter peaks evident for SARS-CoV-2

In spring and summer 2020 and winter 2020-1, SARS-CoV-2 infections parsimoniously followed the pattern of seasonal respiratory viruses, falling away in the summer months and rising again in the autumn, with peaks in deaths occurring between mid-November 2020 and mid-April 2021 in different northern temperate countries.

Although falling infection levels were sometimes prolonged into early summer or began to rise again in late summer, there were no peaks in fatalities in summer or early autumn 2020. 

Most notably, while cases in Sweden rose in a pattern close to the European average in early 2020, they persisted much later, continuing to a plateau in late spring and early summer, before falling away sharply from the end of June. Hospitalisations and deaths fell more smoothly from the mid-April peak, however, and showed no corresponding rise in late spring and early summer.

Similarly, while infections began to rise in late summer in some countries – such as France – there was no substantial increase in deaths before mid-autumn. Summer 2020 appears to have broken the link between infections and serious illness in the absence of vaccination. 

Sweden has so far emerged relatively unaffected by the Delta variant. Although this variant was detected in Sweden – as it was in most other European countries – infections in Sweden nevertheless fell with the onset of summer. As Sweden’s State Epidemiologist Anders Tegnell remarked in an interview on June 18th, 2021 (at about 8 minutes 25 seconds), “the number of cases in Sweden are falling rapidly, very rapidly I would say, much more rapidly than we ever thought was possible”. Tegnell also makes some sceptical points about asymptomatic transmission and mass testing, so beloved of the U.K.’s SAGE committees.

Recent peaks attributable to the Delta variant have occurred in countries such as Denmark, Belgium and the Netherlands, but these outbreaks too may have peaked as they appear to have in the U.K.

SAGE scenarios – anything can happen in the next eight weeks…?

Turning to the latest (July 6th) scenarios of the SAGE’s SPI-M-O modelling groups, we find hospitalisations could be between 50 and 10,000 per day by August 31st depending on the R value. SPI-M-O note these scenarios are not forecasts or predictions, leaving open to question their purpose with regard to Government formulation of policy. 

Previous over-estimations of hospitalisations are attributed to: 1) the cancellation of ‘Freedom Day’ on June 21st permitting more vaccinations to be administered and transmission to be delayed due to restrictions; 2) less than anticipated mixing between adults since late April to mid-May; and 3) the effectiveness of vaccines against the Delta variant.

There appears to be no suggestion of an emphatic effect of spring and summer on behaviour, the virus or viral transmission, which would have been considered conventional wisdom until mid-March 2020.

Warwick University

The Warwick models predict the current rise in hospitalisations will persist to peak in late summer or early autumn, which may or may not be accompanied by a small wave – based on the mean estimates – from late December 2021 or early February 2022 depending on supposed “precautionary behaviour”.

None of the Warwick models predict a fall in hospitalisations in summer 2021 nor – by implication – a fall in infections.

Imperial College London

Imperial College offers two models, based on optimistic (upper figure) and central (lower figure) estimates of vaccine effectiveness, adjusted according to estimates of the speed of change in behaviour and the R value. 

Both models predict peaks in the early autumn, possibly delayed to mid-autumn if changes in behaviour are slow. Using these assumptions, the mean estimates presented for hospitalisations are higher than in the Imperial models. 

Central estimates of vaccine effectiveness with sudden relaxation in precautionary behaviour appears to predict mean daily hospitalisations of about 2,500 to about 12,000 per day by the end of September depending on the R value. Imperial have produced a further model based on pessimistic estimates of vaccine effectiveness (not shown).

Of the Imperial models, only the gradual relaxation of restrictive behaviour scenarios indicate a fall in hospitalisations, but in both instances this simply delays a peak in hospitalisations and – by implication – infections until the early autumn. Neither model anticipates an imminent fall continuing into summer, nor a winter peak between December and February.

London School of Hygiene and Tropical Medicine (LSHTM)

LSHTM present similar models based on a further set of assumptions and predict a peak in hospitalisations in mid-summer, varying in size according to the extent of reduction in transmission (five to 20% reduction at medium mobility is shown in the figure).

Again, the LSHTM model precludes the current reduction to a baseline as in summer 2020.

The ZOE Symptom Study, which provides invaluable independent comparator to reported positives figures, appears to show infections to be rising to July 20th, but only since the method of estimation was revised. Comparators such as ONS and REACT-1 are out of date.

Implications of the models

None of the SAGE models predict a sharp fall and summer lull in infections. Rather, the SAGE report states “the prevalence of infection will almost certainly remain extremely high for at least the rest of the summer”.

We are left with two competing hypotheses:

SAGE predict a continued rise in infections, accompanied by hospitalisations and deaths, peaking in mid-summer or early autumn. There may be a further small wave from late December or early February, or none at all.

Parsimony predicts cases will fall to baseline as summer advances, much as occurred in Sweden last year – a late spring or early summer cold that does not cause significant morbidity or mortality. The summer disappearance will be followed by a resumption in the autumn rising to a peak in infections and deaths in winter proper.

Are the SAGE models already wrong?

Although summer peaks in infections in seasonal respiratory viruses are rare, they are not unknown, particularly in novel varieties and, it may be noted that – unlike in Sweden in 2020 – the spring rise in infections in the U.K. arose from a low base and involved a new variant – the Delta variant – and was preceded by the vaccine roll-out.

While vaccination is argued to be the key factor in keeping hospitalisations and deaths figures low, these measures were also low in the late spring 2020 wave of infections in Sweden. It is possible that nosocomial and care-home outbreaks have also been prevented, in part due to the seasonal fall in general demand for hospital beds in the spring and summer. The most recent ONS report shows overall excess deaths in England and Wales to be higher at home than in care homes or hospitals. Nevertheless, it is striking that reported positives in Scotland have been falling since the end of June.

Hospitalisations in Scotland are also falling from a peak approximately a week later.

The rest of the U.K. is now following the trend in Scotland, which showed a rapid fall in infections from the end of spring and beginning of summer, as Sweden did in 2020. Are we simply experiencing a late impact of seasonality on suppression of spread, which has finally taken effect?

Reported positives peaked just prior to ‘Freedom Day’ in England and about three weeks earlier in Scotland. There is no sign of any stall in the falling trajectory of infections in either country, as could be attributed to the relaxation of restrictions on ‘Freedom Day’. This would be not at all surprising to those who observed the lack of impact of ‘opening up’ in Texas and Florida some months ago.

On the basis of current infection data, the SAGE models are already wrong.

So must be the assumptions of virus transmission and effects of Non-Pharmaceutical Interventions – and lack of effect of nature – on which they are based.

It begs the question as to why the Government and media have again so enthusiastically engaged with consistently disappointing predictions leading to such damaging public health policy.

None of this should be a distraction from the point that lockdowns cause a good deal of harm to physical and mental health and to the economy, far outweighing any presumed benefit – if any can be shown. The models, NPIs and lockdowns are about politics, not science.

The co-authors are a PhD epidemiologist trained at a Russell Group University and a retired former Professor of Forensic Science and Biological Anthropology.

As Infections Plummet Following ‘Freedom Day’ the Models Predicting Catastrophe are Exposed as Fatally Flawed

As reported positive cases plummet following ‘Freedom Day’ – down to 24,950 across the U.K. on Monday, less than half the peak of 54,674 just nine days earlier – the damage limitation among the doomsters begins.

In the Spectator , Professor Oliver Johnson of Bristol University stepped up this morning to try to explain.

He starts by observing that “for the first time in 18 months, there’s been a fall in cases that can’t be easily explained by a national lockdown”. Yet the Spectator recently published an article by Professor Simon Wood showing that new infections peaked and fell before lockdown on all three occasions in England. Did the editors forget to bring it to Professor Johnson’s attention?

Next, Professor Johnson offers some reasons why it may yet be a false dawn.

Indeed it’s possible that the peak in cases, welcome though it is, could only be a local maximum with further rises to come. The rapid reversal in trajectory (from 40% increases between corresponding days of the week to 40% decreases) seems too sudden to be caused by a rapid gain in immunity. It seems more likely to be due to changes in behaviour, with school holidays, the end of the European Championship football and recent hot weather meaning that infected people have had fewer opportunities to spread the disease.

You could have made a similar argument about Covid peaking in Bolton, one of the first places hit by the Delta variant. There was plenty of talk of local herd immunity there. But it’s worth noticing that those falls were subsequently reversed.

And here’s the risk now: what behaviour gives, behaviour can take away. I don’t think anyone can be certain if and when Covid might start going up again. But Scotland gives us hope that sustained falls may be possible.

So far we haven’t even seen the effect of the July 19th reopening in the data, let alone people following now-deleted advice not to ‘cower’, plus there’s the return to schools and universities to come, seasonal effects coming back in the autumn and so on.

The argument that “what behaviour gives, behaviour can take away” is precisely why the models always predict exit waves. Yet the modellers don’t seem to have noticed that these exit waves never happen. There was no exit wave in the U.K. or Europe in summer 2020, nor in spring 2021 in the U.K. as restrictions were eased, nor in the U.S. as measures were lifted. Yet the myth of the exit wave persists.