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Coronavirus Covid-19 Imperial College Public Health England Worldometers

Recent events and Coronavirus model update

Foreward

I am delighted that Roger Penrose, whose lectures I attended back in the late 60s, has become a Nobel laureate. It has come quite late (in his 80s), bearing in mind how long ago Roger, and then Stephen Hawking, had been working in the field of General Relativity, and Black Hole singularities in particular. I guess that recent astronomical observations, and the LIGO detection of gravitational waves at last have inspired confidence in those in Sweden deciding these matters.

I had the privilege, back in the day, of not only attending Roger’s lectures in London, but also the seminars by Stephen Hawking at DAMTP (Department of Applied Maths and Theoretical Physics, now the Isaac Newton Institute) in Cambridge, as well as lectures by Fred Hoyle, Paul Dirac and Martin Rees, amongst other leading lights.

Coming so late for Roger, and not at all, unfortunately, for Stephen Hawking, there is no danger of any “Nobel effect” for them (the tendency of some Nobel laureates either to not achieve much after their “enNobelment”(!) or to apply themselves, with overconfidence, to topics outside their speciality, to little effect, other than in a negative way on their reputation).

The remarkable thing about Roger Penrose is the breadth of his output in many areas of Mathematics over a very long career; and not only that, but the great modesty with which he carries himself. His many books illustrate the breadth of those interests.

I am delighted! If only my work below were worth a tiny fraction of his!

Coronavirus status

Many countries, including the UK, are experiencing a resurgence of Covid-19 cases recently, although, thankfully, with a much lower death rate. This is most likely owing to the younger age range of those being infected, and the greater experience and techniques that medical services have in treating the symptoms. I covered the age dependency in my most recent post on September 22nd, since when there has been a much higher rate of cases, with the death rate also increasing.

Model response

I have run several iterations of my model in the meantime, since my last blog post, as the situation has developed. There has been a remarkable increase in Covid-19 in the USA, as well as in many other countries.

I have introduced several lockdown adjustment points into my UK model, firstly easing the restrictions somewhat, to reflect things such as the return to schools, and other relaxations Governments in the four home UK countries have introduced, followed by some increases in interventions to reflect recent actions such as the “rule of six” and other related measures in the UK.

I’ll just show two charts initially to reflect the current status of the model. I am sure there will be some further “hardening” of interventions (exemplified in a later chart), and so the model forecast outcomes will, I expect, reduce as I introduce these when they come. I have already shown, in my recent post on model sensitivities, that the forecast is VERY sensitive to changes to intervention effectiveness in the model .

The first chart, from Excel, is of the type I have used before to show the cumulative and daily reported and modelled deaths on the same chart:

Model chart showing cumulative and daily UK deaths compared to reported deaths
Model chart showing cumulative and daily UK deaths compared to reported deaths

I have made no postulated interventions beyond October 6th in this model, but I fully expect some imminent interventions to bring down the forecast number of deaths.

The scatter in the orange dots (reported daily deaths) is caused by the regular under-reporting of deaths at weekends, followed by those deaths being added to the reports in the following couple of days of the week. Hence I show a 7-day trend line (the orange line) to smooth that effect.

The successive quantitative changes to the lockdown effectiveness are shown in the chart title, the initial UK lockdown having occurred on March 23rd.

The following chart, plotted straight from the Octave model code, shows the model versions of the lockdown and subsequent interventions in more detail, including dates. It also includes reported and modelled cases as well as deaths data, both cumulative and daily.

Chart 11 showing both cumulative and daily UK model and reported deaths and cases
Chart 11 showing both cumulative and daily UK model and reported deaths and cases

This is quite a busy chart. Again we see the clustering of reported data (this time for reported cases as well as reported deaths) owing to the reporting delays at weekends.

The key feature is the sharp rise in cases, and to a lesser extent, deaths, around the time of the lockdown easing in the summer. The outcomes at the right for April 2021 will be modified (reduced), I believe, by measures yet to be taken that have already been trailed by UK Government.

The forecasts from the model are to the right of the chart, at Day 451, April 26th 2021. The figures presented there are the residual statistics at that point. In the centre of the chart are the reported cumulative and daily figures as at October 8th. The lockdown easing dates and setting percentages are listed in the centre of the chart, in date order.

Data accuracy, and Worldometers

The charts are based on the latest daily updates, and also corrections made in the UK case data, owing to the errors caused at Public Health England (PHE) by the use of a legacy version of the Excel spreadsheet system by some of their staff. That older Excel version loses data, owing to a limit on the number of lines it can handle in a table (c. 64,000 (or, more likely, 216-1) instead of millions in current versions of Excel).

Thus (to increase reader confidence(!)) I haven’t run the Excel chart again for the charts that follow. I am indebted to Dr. Tom Sutton for his Worldometers interrogation script, which allows me to collect Worldometers data and run model changes quickly, with current data, and plot the results, using Python for the data interrogation, and Octave (the GNU free version of MatLab) to run the model and plot results, fed by the UK data from the Worldometers UK page.

Tom’s Python “corona-fetch” code allows me to extract any country’s data rapidly from Worldometers, in which I have some confidence. They updated the UK data, and cast it back to the correct days between September 25th and October 4th, following the UK Government’s initial October 2nd announcement of the errors in their reporting.

Worldometers did this before I was able to find the corrected historic data on the UK Government’s own Coronavirus reporting page – it might not yet even be there for those previous days; the missing data first appeared only as much inflated numbers for the days on that October 2nd-4th weekend.

Case under-reporting

As I highlighted in my September 22nd post, I believe that reported cases are under-reported in the UK by a factor of over 8 – i.e. less than 12.5% of cases are being picked up, in my view, owing to a lack of testing, and the high proportion of asymptomatic infections, resulting in fewer requested tests.

The under-reporting of cases (defining cases as those who have ever had Covid-19) was, in effect, confirmed by the major antibody testing programme, led by Imperial College London, involving over 100,000 people, finding that just under 6% of England’s population – an estimated 3.4 million people – had antibodies to Covid-19, and were therefore likely previously to have had the virus, prior to the end of June.

The USA

For interest, I ran the model for the USA at the same time, as it is so easy to source the USA Worldometers data. Only one lockdown event is shown in my model charts for the US, as I don’t have detailed data for the US on Government actions and population and individual reactions, on which I have done more work for the UK – the USA not being my principal focus.

I would expect there should be some intervention easing settings in the summer period for the USA, judging by what we have seen of the growth in the USA’s numbers of cases and deaths during that period.

Those relaxations, both at state level and individually, have, in my view, frustrated many forecasts (some made somewhat rashly, and not couched with caveats), including the one by Michael Levitt made as recently as mid-July for August 25th (to which I referred in some detail in my September 2nd post) when both the quantum of the US numbers, and the upwards slope for deaths and cases were quite contrary to his expectation. We can see that reflected in my model’s unamended figures, following the 74% effective March 24th lockdown event, representing the first somewhat serious reaction to the epidemic in the USA.

This is the problem, in my view, with curve-fitting (phenomenological) forecasts used on their own, as compared with mechanistic models such as mine, whose code was originally developed by Prof. Alex de Visscher at Concordia University.

All that curve-fitting is does is to perform a least-squares fit of a 3 or 4 parameter Logistics curve of some kind (Sigmoid, Roberts or Gompertz curve) top-down, with no bottom-up way to reflect Government strategies and population/individual reactions. Curve-fitting can give a fast graphical interpolation of data, but isn’t so suitable for extrapolating a forecast of any worthwhile duration.

This chart below, without the benefit of the introduction of subsequent intervention measures, shows how a forecast can begin to undershoot reality, until the underlying context can be introduced. Lockdown easing events (both formal and informal since March 24th) need to be added to allow the model to show their potential consequences for increased cases and deaths, and thus for the model to be calibrated for projections beyond the present day, October 8th.

Chart 11 showing both cumulative and daily US model and reported deaths and cases
Chart 11 showing both cumulative and daily US model and reported deaths and cases

Effect of a UK “circuit-breaker” intervention

There is current discussion of a (2 week) “circuit-breaker” partial lockdown in the UK, coinciding with schools’ half-term, and the Government seems to be considering a tiered version of this, with the areas with higher caseloads making stricter interventions. There would be differences in the policy within the four home UK countries, but all of them have interventions in mind, for that half-term period, as cases are increasing in them all.

I have postulated, therefore, an exemplar increased intervention. I have applied a 10% increase in current intervention effectiveness on October 19th (although there are some differences in the half-term dates across the UK), followed by a partial relaxation after 2 weeks, -5%, reducing the circuit-breaker measure by half – so not back to the level we are at currently.

Here is the effect of that change on the model forecast.

Chart 11 showing the effect on cumulative and daily UK model and reported deaths and cases of a 2-week circuit-breaker measure on October 19th
Chart 11 showing the effect on cumulative and daily UK model and reported deaths and cases of a 2-week circuit-breaker measure on October 19th

As one might expect for an infection with a 7-14 day incubation period, although the effect on reducing new infections (daily cases) is fairly rapid, this is lagged somewhat by the effect on the death rate; but over the medium and longer term, this change, just as for the original lockdown, reduces the severity of the modelled outcome materially.

I don’t think any models have the capability yet to reflect very detailed interventions, local and regional as they are becoming, to deal with local outbreaks in a context where much of the country is less affected. What we have been seeing are what I have called “multiple superspreader” events, and potentially a new modelling methodology, reflecting Adam Kucharski’s “k-number” concept of over-dispersion would be needed. I covered this in more detail in my August 4th blog post.

Discussion

As I reported in my blog post on May 14th, if the original lockdown had been 2 weeks earlier than March 23rd (and this principle was supported in principle by scientists reporting to the Parliamentary Science and Technology Select Committee on June 10th, which I reported in my blog post on June 11th), there would have been far fewer deaths; the UK Government is likely to want to avoid any delay this time around.

October 19th might well be later than they would wish, and so earlier interventions, varying locally and/or regionally are likely.

While the forecast of a model is critically dependent not only on the model logic, and its virus infectivity parameters, the decisions to be taken about interventions, and their timing, critically impact the epidemic and the modelled outcomes.

A model like this offers a way to calibrate and test the effect of different changes. My model does that in a rather broad-brush way, using successive broad intervention effectiveness parameters at chosen times.

Imperial College analysis

Models used by Government advisers are more sophisticated, and as I reported last time, the Imperial College data sources, and their model codes are available on their website at https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/. Both Imperial College and Harvard University have published their outlook on cyclical behaviour of the pandemic; in the Imperial case, the triggering of interventions and any relaxations were modelled on varying ICU bed occupancy, but it could be also be done, I suppose, though R-number thresholds (upwards and downwards) at any stage. Here is the Imperial chart; the Harvard one was similar, projected into 2022.

The potentially cyclical caseload from Covid-19, with interventions and relaxations applied as ICU bed demand changes
The potentially cyclical caseload from Covid-19, with interventions and relaxations applied as ICU bed demand changes

The Imperial computer codes are written in the R language, which I have downloaded, as part of my own research, so I look forward to looking at them and reporting later on.

I know that their models allow very detailed analysis of options such as social distancing, home isolation and/or quarantining, schools/University closure and many other possible interventions, as can be seen from the following chart which I have shown before, from the pivotal and influential March 16th Imperial College paper that preceded the first UK national lockdown on March 23rd.

It is usefully colour-coded by the authors so that the more and less effective options can be more easily discerned.

PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)
PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)

An intriguing point is that in this chart (on the very last page of the paper, and referenced within it) the effectiveness of the three measures “CI_HQ_SD” in combination (home isolation of cases, household quarantine & large-scale general population social distancing) taken together (orange and yellow colour coding), was LESS than the effectiveness of either CI_HQ or CI_SD taken as a pair of interventions (mainly yellow and green colour coding)?

The answer to my query, from Imperial, was along the following lines, indicating the care to be taken when evaluating intervention options.

It’s a dynamical phenomenon. Remember mitigation is a set of temporary measures. The best you can do, if measures are temporary, is go from the “final size” of the unmitigated epidemic to a size which just gives herd immunity.

If interventions are “too” effective during the mitigation period (like CI_HQ_SD), they reduce transmission to the extent that herd immunity isn’t reached when they are lifted, leading to a substantial second wave. Put another way, there is an optimal effectiveness of mitigation interventions which is <100%.

That is CI_HQ_SDOL70 for the range of mitigation measures looked at in the report (mainly a green shaded column in the table above).

While, for suppression, one wants the most effective set of interventions possible.

All of this is predicated on people gaining immunity, of course. If immunity isn’t relatively long-lived (>1 year), mitigation becomes an (even) worse policy option.

This paper (and Harvard came to similar conclusions at that time, as we see in the additional chart below) introduced (to me) the potential for a cyclical, multi-phase pandemic, which I discussed in my April 22nd report of the Cambridge Conversation I attended, and here is the relevant illustration from that meeting.

Imperial College and Harvard forecasts and illustrations of cyclical pandemic behaviour
Imperial College and Harvard forecasts and illustrations of cyclical pandemic behaviour

In the absence of a pharmaceutical solution (e.g. a vaccine) this is all about the cyclicity of lockdown followed by easing; then the population’s and pandemic’s responses; and repeats of that loop, just what we are beginning to see at the moment.

Second opinion on the Imperial model code

Scientists at the School of Physics and Astronomy, University of Edinburgh have used the Imperial College CovidSim code to run the data and check outcomes, reported in the British Medical Journal (BMJ), in their paper Effect of school closures on mortality from coronavirus disease 2019: old and new predictions.

Their conclusions were broadly supportive of the veracity of the modelling tool, and commenting on their results, they say:

The CovidSim model would have produced a good forecast of the subsequent data if initialised with a reproduction number of about 3.5 for covid-19. The model predicted that school closures and isolation of younger people would increase the total number of deaths, albeit postponed to a second and subsequent waves. The findings of this study suggest that prompt interventions were shown to be highly effective at reducing peak demand for intensive care unit (ICU) beds but also prolong the epidemic, in some cases resulting in more deaths long term. This happens because covid-19 related mortality is highly skewed towards older age groups. In the absence of an effective vaccination programme, none of the proposed mitigation strategies in the UK would reduce the predicted total number of deaths below 200 000.

Their overall conclusion was:

It was predicted in March 2020 that in response to covid-19 a broad lockdown, as opposed to a focus on shielding the most vulnerable members of society, would reduce immediate demand for ICU beds at the cost of more deaths long term. The optimal strategy for saving lives in a covid-19 epidemic is different from that anticipated for an influenza epidemic with a different mortality age profile.

This is consistent with the table above, and with the explanation given to me by Imperial quoted above. The lockdown can be “too good” and optimisation for the medium/long term isn’t the same as short term optimisation.

I intend to run the Imperial code myself, but I am very glad to see this second opinion. There have been many responses to it, so I will devote a later blog post to it.

Concluding Comments

As we see, a great deal of multidisciplinary work is proceeding in many Universities and other organisations around the world. Virologists, epidemiologists, clinicians, mathematicians and many others are involved in working out solutions to the issues raised in all countries by the SARS-Cov-2 pandemic.

A vaccine must be top of the list for dealing with it, and until then, the best that we can do as members of the public is to recognise the key indicators for staying safe, some of them mentioned above in relation to the NPIs.

We have seen that in the spring and summer period it was possible to make progress with opening up the economy, but as the easing of interventions begins to coincide with autumn, the return to schools and Universities, and the increasing pressure to revive not just our economy, but also social interactions, cases have increased, and the test will continue to be how to control the spread of the virus while allowing some “normal” activities to return.

The studies I have mentioned, as well as my own work indicate clearly the complexity, and in some respects the counter-intuitive nature of managing the epidemic. There is much more to do.

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Coronavirus Covid-19 Herd Immunity Imperial College Michael Levitt Office for National Statistics ONS PHE Public Health England Superspreader Sweden

Model update following UK revision of Covid-19 deaths reporting

Introduction

On August 12th, the UK Government revised its counting methodology and reporting of deaths from Covid-19, bringing Public Health England’s reporting into line with that from the other home countries, Wales, Northern Ireland and Scotland. I have re-calibrated and re-forecast my model to adapt to this new basis.

Reasons for the change

Previously reported daily deaths in England had set no time limit between any individual’s positive test for Covid-19, and when that person died. 

The three other home countries in the UK applied a 28-day limit for this period. It was felt that, for England, this lack of a limit on the time duration resulted in over-reporting of deaths from Covid-19. Even someone who had died in a road accident, say, would have been reported as a Covid-19 death if they had ever tested positive, and had then recovered from Covid-19, no matter how long before their death this had happened.

This adjustment to the reporting was applied retroactively in England for all reported daily deaths, which resulted in a cumulative reduction of c. 5,000 in the UK reported deaths to up to August 12th.

The UK Government say that it is also to report on a 60-day basis (96% of Covid-19 deaths occur within 60 days and 88% within 28 days), and also on the original basis for comparisons, but these two sets of numbers are not yet available.

On the UK Government’s web page describing the data reporting for deaths, it says “Number of deaths of people who had had a positive test result for COVID-19 and died within 28 days of the first positive test. The actual cause of death may not be COVID-19 in all cases. People who died from COVID-19 but had not tested positive are not included and people who died from COVID-19 more than 28 days after their first positive test are not included. Data from the four nations are not directly comparable as methodologies and inclusion criteria vary.

As I have said before about the excess deaths measure, compared with counting deaths attributed to Covid-19, no measure is without its issues. The phrase in the Government definition above “People who died from COVID-19 but had not tested positive are not included…” highlights such a difficulty.

Model changes

I have adapted my model to this new basis, and present the related charts below.

  • Model forecast for the UK deaths as at August 14th, compared with reported for 84.3% lockdown effectiveness, on March 23rd, modified in 5 steps by -.3%, -0% -0% and -0% successively
  • Model forecast for the UK deaths as at August 14th, compared with reported for 84.3% lockdown effectiveness, modified in 5 steps by -.3%, -0% -0% and -0% successively
  • Model forecast for the UK deaths as at August 14th, compared with reported for 84.3% lockdown effectiveness, on March 23rd, modified in 5 steps by -.3%, -0% -0% and -0% successively
  • Model forecast for the UK deaths as at August 14th, compared with reported for 84.3% lockdown effectiveness, on March 23rd, modified in 5 steps by -.3%, -0% -0% and -0% successively
  • Model forecast for the UK deaths as at August 14th, compared with reported for 84.3% lockdown effectiveness, on March 23rd, modified in 5 steps by -.3%, -0% -0% and -0% successively
  • Chart 12 for the comparison of cumulative & daily reported & modelled deaths to 26th April 2021, adjusted by -.3% on May 13th

This changed reporting basis reduced the cumulative UK deaths to August 12th from 46,706 to 41,329, a reduction of 5,377.

The fit of my model was better for the new numbers, requiring only a small increase in the initial March 23rd lockdown intervention effectiveness from 83.5% to 84.3%, and a single easing reduction to 84% on May 13th, to bring the model into good calibration up to August 14th.

It does bring the model forecast for the long term plateau for deaths down to c. 41,600, and, as you can see from the charts above, this figure is reached by about September 30th 2020.

Discussion

The relationship to case numbers

You can see from the first model chart that the plateau for “Recovered” people is nearly 3 million, which implies that the number of cases is also of the order of 3 million. This startling view is supported by a recent antibody study reported by U.K. Government here.

This major antibody testing programme, led by Imperial College London, involving over 100,000 people, found that just under 6% of England’s population – an estimated 3.4 million people – had antibodies to COVID-19, and were likely to have previously had the virus prior to the end of June.

The reported numbers in the Imperial College study could seem quite surprising, therefore, given that 14 million tests have been carried out in the U.K., but with only 313,798 positive tests reported as at 12th August (and bearing in mind that some people are tested more than once).

But the study is also in line with the estimate made by Prof. Alex de Visscher, author of my original model code, that the number of cases is typically under-reported by a factor of 12.5 – i.e. that only c. 8% of cases are detected and reported, an estimate assessed in the early days for the Italian outbreak, at a time when “test and trace” wasn’t in place anywhere.

A further sanity check on my modelled case numbers, relative to the number of forecasted deaths, would be on the observed mortality from Covid-19 where this can be assessed.

A study by a London School of Hygiene & Tropical Medicine team carried out an analysis of the Covid-19 outbreak in the closed community of the Diamond Princess cruise ship in March 2020.

Adjusting for delay from confirmation-to-death, this paper estimated case and infection fatality ratios (CFR, IFR) for COVID-19 on the Diamond Princess ship as 2.3% (0.75%-5.3%) and 1.2% (0.38-2.7%) respectively.

In broad terms, my model forecast of 42,000 deaths and up to 3 million cases would be a ratio of about 1.4%, and so the relationship between the deaths and cases numbers in my charts doesn’t seem to be unreasonable.

Changing rates of infection

I am not sure whether the current forecast for a further decline in the death rate will remain, in the light of continuing lockdown easing measures, and the local outbreaks.

Both the Office for National Statistics (ONS) and Public Health England (PHE) reported in early July a drop in the rate of decline in Covid-19 cases per 100,000 people in England.

Figure 2: The latest exploratory modelling shows the downward trend in those testing positive for COVID-19 has now levelled off

This was at the same time as the ONS reported that excess deaths have reduced to a level at or below the average for the last five years.

The number of deaths involving COVID-19 decreased for the 10th consecutive week

PHE reports this week that the infection rate is now more pronounced for under-45s than for over-45s, a reversal of the situation earlier in the pandemic. Overall case rates, however, remain lower than before; and although the rate of decline in the case rate has slowed for-over-45s, and is nearly flat now, for under-45s the infection rate has started to increase slightly.

Covid-19 cases rate of decline slows more for under-45s

The impact on the death rate might well be lower than previously, owing to the lower fatality rates for younger people compared with older people.

Herd immunity

Closely related to the testing for Covid-19 antibodies is herd immunity, a topic I covered in some detail on my blog post on June 28th, when I discussed the relative positions of the USA and Europe with regard to the spike in case numbers the USA was experiencing from the middle of June, going on to talk about the Imperial College Coronavirus modelling, led by Prof. Neil Ferguson, and their pivotal March 16th paper.

This paper was much criticised by Prof Michael Levitt, and others, for the hundreds of thousands of deaths it mentioned if no action were taken, cited as scare-mongering, ignoring to some extent the rest of what I think was a much more nuanced paper than was appreciated, exploring, as it did, the various interventions that might be taken as part of what has become known as “lockdown”.

The intervention options were also quite nuanced, embracing as they did (with outcomes coded as they were in the chart below) PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions).

PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)
PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)

I had asked the lead author of the paper why the effectiveness of the three measures “CI_HQ_SD” in combination (home isolation of cases, household quarantine & large-scale general population social distancing) taken together (orange and yellow colour coding), was LESS than the effectiveness of either CI_HQ or CI_SD taken as a pair of interventions (mainly yellow and green colour coding)?

The answer was in terms of any subsequent herd immunity that might or might not be conferred, given that any interventions as part of a lockdown strategy would be temporary. What would happen when they ceased?

The issue was that if the lockdown measures were too effective, then (assuming there were any immunity to be conferred for a usefully long period) the potential for any subsequent herd immunity would be reduced with too successful a lockdown. If there were no worthwhile period of immunity from catching Covid-19, then yes, a full lockdown would be no worse than any other partial strategy.

Sweden

I mention all this as background to a paper that was just published in the Journal of the Royal Society of Medicine as I started this blog post, on August 12th. It concerns the reasons why, as the paper authored by Eric Orlowski and David Goldsmith asserts, that four months into the COVID-19 pandemic, Sweden’s prized herd immunity is nowhere in sight.

This is a somewhat polemical paper, as Sweden is often held up as an example of how countries can succeed in combating the SARS-Cov-2 pandemic by emulating Sweden’s non-lockdown approach. I have been, and remain surprised by such claims, and now this paper helps calibrate and articulate the underlying reasons.

Although compared with the UK, Sweden had done little worse, if at all, despite resisting the lockdown approach (although its demographics and lifestyle characteristics are not necessarily comparable to the UK’s), compared with their more similar nearest neighbours, Norway, Denmark and Finland, Sweden has done far worse in terms of deaths and deaths per capita.

I think that either for political or for other related reasons, perhaps economic ones, even some otherwise sensible scientists are advocating the Swedish approach, somehow ignoring the more valid (and negative) comparisons between Sweden and the other Scandinavian countries, as opposed to more favourable comparisons with others further afield – the UK, for example.

I have tried to remain above the fray, notably on the Twittersphere, but, at least on my own blog, I want to present what I see as a balanced assessment of the evidence.

That balance, in this case, strikes me like this: if there were an argument for the Swedish approach, then a higher level of herd immunity would have been the payoff for experiencing more immediate deaths in favour of a better outcome later.

But that doesn’t seem to have happened, at least in terms of outcomes from testing for antibodies, as presented in this paper. As it says “it is clear that nowhere is the prevalence of IgG seropositivity high (the maximum being around 20%) or climbing convincingly over time. This is especially clear in Sweden, where the authorities publicly predicted 40% seroconversion in Stockholm by May 2020; the actual IgG seroprevalence was around 15%.

Concluding comments

As I said in my August 4th post, the outbreaks we are seeing in some UK localities (Leicester, Manchester, Aberdeen and many others) seem to be the outcome of individual and multiple local super-spreading events.

These are quite hard to model, requiring very fine-grained data regarding the types and extent of population interactions, and the different effects of a range of intervention measures available nationally and locally, as I mentioned above, applied in different places at different times.

The reproduction number, R (even nationally) can be increased noticeably by such localised events, because of the lower overall incidence of cases in the UK (something we have seen in some other countries too, at this phase of the pandemic).

While most people nationally aren’t directly affected by these localised outbreaks, I believe that caution – social distancing where possible, for example – is still necessary.

Categories
Coronavirus Covid-19 Office for National Statistics ONS PHE Public Health England Worldometers

The effect of lockdown easing in the UK

Introduction

As reported in my previous post, there has been a gradual reduction in the rate of decline of cases and deaths in the UK relative to my model forecasts. This decline had already been noted, as I reported in my July 6th blog article, by The Office for National Statistics and their research partners, the University of Oxford, and reported on the ONS page here.

I had adjusted the original lockdown effectiveness in my model (from 23rd March) to reflect this emerging change, but as the model had been predicting correct behaviour up until mid-late May, I will present here the original model forecasts, compared with the current reported deaths trend, which highlights the changes we have experienced for the last couple of months.

Forecast comparisons

The ONS chart which highlighted this slowing down of the decline, and even a slight increase, is here:

Figure 6: The latest exploratory modelling shows incidence appears to have decreased between mid-May and early June
Figure 6: The latest exploratory modelling shows incidence appears to have decreased between mid-May and early June

Public Health England had also reported on this tendency for deaths on 6th July:

The death rate trend can be seen in the daily and 7-day average trend charts, with data from Public Health England
The death rate trend can be seen in the daily and 7-day average trend charts

The Worldometers forecast for the UK has been refined recently, to take account of changes in mandated lockdown measures, such as possible mask wearing, and presents several forecasts on the same chart depending on what take-up would be going forward.

Worldometers forecast for the UK as at July 31st 2020
Worldometers forecast for the UK as at July 31st 2020

We see that, at worst, the Worldometers forecast could be for up to 60,000 deaths by November 1st, although, according to their modelling, if masks are “universal” then this is reduced to under 50,000.

Comparison of my forecast with reported data

My two charts that reveal most about the movement in the rate of decline of the UK death rate are here…

On the left, the red trend line for reported daily deaths shows they are not falling as fast as they were in about mid-May, when I was forecasting a long term plateau for deaths at about 44,400, assuming that lockdown effectiveness would remain at 83.5%, i.e. that the virus transmission rate was reduced to 16.5% of what it would be if there were no reductions in social distancing, self isolation or any of the other measures the UK had been taking.

The right hand chart shows the divergence between the reported deaths (in orange) and my forecast (in blue), beginning around mid to late May, up to the end of July.

The forecast, made back in March/April, was tracking the reported situation quite well (if very slightly pessimistically), but around mid-late May we see the divergence begin, and now as I write this, the number of deaths cumulatively is about 2000 more than I was forecasting back in April.

Lockdown relaxations

This period of reduction in the rate of decline of cases, and subsequently deaths, roughly coincided with the start of the UK Govenment’s relaxation of some lockdown measures; we can see the relaxation schedule in detail at the Institute for Government website.

As examples of the successive stages of lockdown relaxation, in Step 1, on May 13th, restrictions were relaxed on outdoor sport facilities, including tennis and basketball courts, golf courses and bowling greens.

In Step 2, from June 1st, outdoor markets and car showrooms opened, and people could leave the house for any reason. They were not permitted to stay overnight away from their primary residence without a ‘reasonable excuse’.

In Step 3, from 4th July, two households could meet indoors or outdoors and stay overnight away from their home, but had to maintain social distancing unless they are part of the same support bubble. By law, gatherings of up to 30 people were permitted indoors and outdoors.

These steps and other detailed measures continued (with some timing variations and detailed changes in the devolved UK administrations), and I would guess that they were anticipated and accompanied by a degree of informal public relaxation, as we saw from crowded beaches and other examples reported in the press.

Model consequences

I did make a re-forecast, reported on July 6th in my blog article, using 83% lockdown effectiveness (from March 23rd).

Two issues remained, however, while bringing the current figures for July more into line.

One was that, as I only have one place in the model that I change the lockdown effectiveness, I had to change it from March 23rd (UK lockdown date), and that made the intervening period for the forecast diverge until it converged again recently and currently.

That can be seen in the right hand chart below, where the blue model curve is well above the orange reported data curve from early May until mid-July.

The long-term plateau in deaths for this model forecast is 46,400; this is somewhat lower than the model would show if I were to reduce the % lockdown effectiveness further, to reflect what is currently happening; but in order to achieve that, the history during May and June would show an even larger gap.

The second issue is that the rate of increase in reported deaths, as we can also see (the orange curve) on the right-hand chart, at July 30th, is clearly greater than the model’s rate (the blue curve), and so I foresee that reported numbers will begin to overshoot the model again.

In the chart on the left, we see the same red trend line for the daily reported deaths, flattening to become nearly horizontal at today’s date, July 31st, reflecting that the daily reported deaths (the orange dots) are becoming more clustered above the grey line of dots, representing modelled daily deaths.

As far as the model is concerned, all this will need to be dealt with by changing the lockdown effectiveness to a time-dependent variable in the model differential equations representing the behaviour of the virus, and the population’s response to it.

This would allow changes in public behaviour, and in public policy, to be reflected by a changed lockdown effectiveness % from time to time, rather than having retrospectively to apply the same (reduced) effectiveness % since the start of lockdown.

Then the forecast could reflect current reporting, while also maintaining the close fit between March 23rd and when mitigation interventions began to ease.

Lockdown, intervention effectiveness and herd immunity

In the interest of balance, in case it might be thought that I am a fan of lockdown(!), I should say that higher % intervention effectiveness does not necessarily lead to a better longer term outlook. It is a more nuanced matter than that.

In my June 28th blog article, I covered exactly this topic as part of my regular Coronavirus update. I referred to the pivotal March 16th Imperial College paper on Non-Pharmaceutical Interventions (NPIs), which included this (usefully colour-coded) table, where green is better and red is worse,

PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)
PC=school and university closure, CI=home isolation of cases, HQ=household quarantine, SD=large-scale general population social distancing, SDOL70=social distancing of those over 70 years for 4 months (a month more than other interventions)

which provoked me to re-confirm with the authors (and as covered in the paper) the reasons for the triple combination of CI_HQ_SD being worse than either of the double combinations of measures CI_HQ or CI_SD in terms of peak ICU bed demand.

The answer (my summary) was that lockdown can be too effective, given that it is a temporary state of affairs. When lockdown is partially eased or removed, the population can be left with less herd immunity (given that there is any herd immunity to be conferred by SARS-Cov-2 for any reasonable length of time, if at all) if the intervention effectiveness is too high.

Thus a lower level of lockdown effectiveness, below 100%, can be more effective in the long term.

I’m not seeking to speak to the ethics of sustaining more infections (and presumably deaths) in the short term in the interest of longer term benefits. Here, I am simply looking at the outputs from any postulated inputs to the modelled epidemic process.

I was as surprised as anyone when, in a UK Government briefing, in early March, before the UK lockdown on March 23rd, the Chief Scientific Adviser (CSA, Sir Patrick Vallance), supported by the Chief Medical Officer (CMO, Prof. Chris Whitty) talked about “herd immunity” for the first time, at 60% levels (stating that 80% needing to be infected to achieve it was “loose talk”). I mentioned this in my May 29th blog post.

The UK Government focus later in March (following the March 16th Imperial College paper) quickly turned to mitigating the effect of Covid-19 infections, as this chart sourced from that paper indicates, prior to the UK lockdown on March 23rd.

Projected effectiveness of Covid-19 mitigation strategies, in relation to the utilisation of critical care (ICU) bedsProjected effectiveness of Covid-19 mitigation strategies, in relation to the utilisation of critical care (ICU) beds
Projected effectiveness of Covid-19 mitigation strategies, in relation to the utilisation of critical care (ICU) beds

This is the imagery behind the “flattening the curve” phrase used to describe this phase of the UK (and others’) strategy.

Finally, that Imperial College March 16th paper presents this chart for a potentially cyclical outcome, until a Covid-19 vaccine or a significantly effective pharmaceutical treatment therapy arrives.

The potentially cyclical caseload from Covid-19, with interventions and relaxations applied as ICU bed demand changes
The potentially cyclical caseload from Covid-19, with interventions and relaxations applied as ICU bed demand changes

In this new phase of living with Covid-19, this is why I want to upgrade my model to allow periodic intervention effectiveness changes.

Conclusions

The sources I have referenced above support the conclusion in my model that there has been a reduction in the rate of decline of deaths (preceded by a reduction in the rate of decline in cases).

To make my model relevant to the new situation going forward, when lockdowns change, not only in scope and degree, but also in their targeting of localities or regions where there is perceived growth in infection rates, I will need to upgrade my model for variable lockdown effectiveness.

I wouldn’t say that the reduction of the rate of decline of cases and deaths is evidence of a “second wave”, but is rather the response of a very infective agent, which is still with us, to infect more people who are increasingly “available” to it, owing to easing of some of the lockdown measures we have been using (both informally by the public and formally by Government).

To me, it is evidence that until we have a vaccine, we will have to live with this virus among us, and take reasonable precautions within whatever envelope of freedoms the Government allow us.

We are all in each others’ hands in that respect.