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Alex de Visscher Coronavirus Covid-19 Easing

A brief look at model sensitivities to lockdown easing as we prepare for winter

Introduction

This is a very brief look at the model I have been working with for the last few months (thanks again to Prof Alex de Visscher for his original work on the model) to illustrate the sensitivities to lockdown easing settings as we move forward.

The UK Government has just announced some reversals of the current easings, and so before I model the new, additional interventions announced today, I want to illustrate quickly the behaviour of the model in response to changing the effectiveness of current interventions, to reflect the easings that have been made.

The history of UK Government changes, policies and announcements relating to Covid-19 be seen here at the Health Foundation website

Charts direct from the model

I can launch my Octave (MatLab) model direct from the Python code (developed by Dr. Tom Sutton) that interrogates the Worldometers UK reports. Similar information for the any country is available on related pages using the appropriate country code extension, eg for the US here.

The dates, cases and deaths data from Tom’s code are passed to the Octave model , which compares the reported data to the model data and plots charts accordingly.

I am showing just one chart 9, for brevity, in six successive versions as a slideshow, which makes it very clear how the successive relaxations of Government interventions (and public behaviour) are represented in the model, and affect the future forecast.

  • Model and reported UK deaths and cases from Feb 1st to Sep 12th with just one easing of .03% after the initial lockdown effectiveness of 84.3%, as shown on the chart
  • Model and reported UK deaths and cases from Feb 1st to Sep 17th with 3 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart
  • Model and reported UK deaths and cases from Feb 1st to Sep 17th with 4 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart
  • Model and reported UK deaths and cases from Feb 1st to Sep 18th with 4 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart
  • Model and reported UK deaths and cases from Feb 1st to Sep 20th with 5 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart
  • Model and reported UK deaths and cases from Feb 1st to Sep 21st with 4 easings and 1 increase after the initial lockdown effectiveness of 84.3%, as shown on the chart

By allowing the slideshow to run, we can see that the model is quite sensitive to the recent successive relaxations of epidemic interventions from Day 155 to Day 227 (July 4th to September 14th).

Charts from the model via spreadsheet analysis

I now show another view of the same data, this time plotted from a spreadsheet populated from the same Octave model, but with daily data plotted on the same charts, offering a little more insight.

  • Model and reported UK deaths and cases from Feb 1st to Sep 12th with just one easing of .03% after the initial lockdown effectiveness of 84.3%, as shown on the chart title
  • Model and reported UK deaths and cases from Feb 1st to Sep 17th with 3 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart title
  • Model and reported UK deaths and cases from Feb 1st to Sep 18th with 4 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart title
  • Model and reported UK deaths and cases from Feb 1st to Sep 20th with 5 easings after the initial lockdown effectiveness of 84.3%, as shown on the chart title
  • Model and reported UK deaths and cases from Feb 1st to Sep 21st with 4 easings and 1 increase after the initial lockdown effectiveness of 84.3%, as shown on the chart title

Here, as well as the cumulative data, we see from the orange dots the scatter of daily reported deaths data (principally caused by lagged data reporting at weekends, with corresponding (upwards) correction in the following days) but also appearing more significant than it really is, because it is plotted at the lower part of the log scale, where the numbers are quite small for the amount of y-axis used to represent them (owing to the log scaling to fit both cumulative and daily reporting on the same chart).

As before, allowing the slideshow to play illustrates the marked effect on the forecast of the increases resulting from the easing of interventions, represented by the % changes to the intervention effectiveness.

This intervention effectiveness started at 84.3%, but on September 20th it was standing at only (84.3 -0.3 -4 -4 -4 -2)% = 70%, although in the last chart I have allowed a 2% increase to reflect some initial UK Government measures to get the virus under control again.

Discussion

The impact of easing of some interventions

As we can see from the model charts, with the UK lockdown relaxation (easing) status as at the last easing point in either presentation, September 14th, there is a quite significant upward tick in the death rate, which follows the earlier upward trend of cases in the UK, previously reported in my most recent post on September 2nd.

It is quite clear to me, in the charts and from the modelling behind them, that the UK’s lockdown, and subsequent series of easing points, has had a marked effect on the epidemic infection rate in the UK. Earlier modelling indicated that had the lockdown been a week or two earlier (I postulated and modelled a March 9th lockdown in particular, and discussed it in two posts on May 14th and June 11th), there would have been far fewer deaths from Covid-19. Prof. Neil Ferguson made this point in his answers to questions at the UK Parliamentary Science & Technology Select Committee on June 10th, as reported in my June 11th post.

Lately, we see that UK Government easing of some aspects of the March 23rd interventions is accompanied by an increase in case (infection) rates, which although more prevalent in the younger, working and socialising population, with a much lower risk of death, is feared to spill over into older parts of the population through families and friends; hence the further UK interventions to come on 24th September.

I am sure that these immediate strategies for controlling (“suppressing”) the epidemic are based on advice from the Scientific Advisory Group for Emergencies (SAGE), and through them by the Scientific Pandemic Influenza Group on Modelling (SPI-M) of which Neil Ferguson and his Imperial College group are part. Sir Patrick Vallance (Chief Scientific Adviser) and Prof. Chris Whitty (Chief Medical Officer), who sit on SAGE, made their own TV presentation direct to the public (with no politicians and no press questions) on 22nd September, outlining the scientific and medical opinions about where we are and where the epidemic is going.

Returning to the modelling, I am happy to see that 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/. The 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 always take time to mention the pivotal and influential March 16th Imperial College paper that preceded the first UK national lockdown on March 23rd, and the table from it that highlighted the many Non Pharmaceutical Interventions (NPIs) available to Government, and their relative effectiveness alone and in combinations.

I want to emphasise that in this paper, many optional strategies for interventions were considered, and critics of what they see as pessimistic forecasts of deaths in the paper have picked out the largest numbers, in the case of zero or minimal interventions, as if this were the only outcome considered.

The paper is far more nuanced than that, and the table below, while just one small extract, illustrates this. You can see the very wide range of possible outcomes depending on the mix of interventions applied.

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)

This paper (and Harvard came to similar conclusions at that time) 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. This is all about the cyclicity of lockdown followed by easing, the population’s and pandemic’s responses, and repeats of that loop, just what we are seeing at the moment.

Cyclical pandemic behaviour
Cyclical pandemic behaviour

Key, however, to good modelling is good data, and this is changing all the time. The fine-grained nature of data about schools, travel patterns, work/home locations and the virus behaviour itself are quite beyond an individual to amass. It does require the resources of teams like those at Imperial College, the London School of Hygiene and Tropical Medicine, and in the USA, Harvard, Johns Hopkins and Washington Universities, to name just some prominent ones, whose groups embrace virological, epidemiological and mathematical expertise as well as (presumably) teams of research students to do much of the sifting of data.

Inferences for model types

In my September 2nd recent post, I drew some conclusions from my earlier investigation into mechanistic (bottom-up) and phenomenological/statistical (exemplified by curve-fitting) modelling techniques. I made it clear that the curve-fitting on its own, while indicative, offers no capability to model intervention methods yet to be made, nor changes in population and individual responses to those Government measures.

In discussing this with someone the other day, he usefully summarised such methods thus: “curve-fitting and least-squares fitting is OK for interpolation, but not for extrapolation”.

The ability in a model to reflect planned or postulated changes to intervention strategies and population responses is vital, as we can see from the many variations made in my model at the various lockdown easing points. Such mechanistic models – derived from realistic infection rates – also allow the case rates and resulting death rates to be assessed bottom-up as a check on reported figures, whereas curve-fitting models are designed only to fit the reported data (unless an overarching assumption is made about under-reporting).

The model shows up this facet of the UK reporting. As in many other countries, there is gross under-estimation of cases, partly because of the lack of a full test and trace system, and partly because testing is not universal. My model is forecasting much nearer to the realistic number of cases, as you will see below; conservatively, the reported numbers are only 10% of the likely infections, probably less.

My final model chart 10, where I have applied an 8.3 multiple to the reported cases to bring them into line with the model, illustrates this. You can just see from the chart, and of course from the daily reported numbers themselves at https://coronavirus.data.gov.uk, that the reported cases are already increasing sharply.

Model and reported UK deaths and cases from Feb 1st to Sep 21st with 4 easings and 1 increase after the initial lockdown effectiveness of 84.3%, as shown on the chart, compared with under-reported cases
Model and reported UK deaths and cases from Feb 1st to Sep 21st with 5 easings and 1 increase after the initial lockdown effectiveness of 84.3%, compared with under-reported cases

You can see from Chart 10 that the plateau for modelled cases is around 3 million. 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.

In this way, mechanistic models can highlight such deficiencies in reporting, as well as modelling the direct effects of intervention measures.

Age-dependency of risk

I have reported before on the startling age dependency of the risk of dying from Covid-19 once contracting it, most recently in my blog post on September 2nd where this chart appeared, amongst others.

UK weekly confirmed cases by age, published by The Times September 5th 2020
UK weekly confirmed cases by age, published by The Times September 5th 2020

I mention this because the recent period of increasing cases in the UK, but with apparently a lower rate of deaths (although the deaths lag cases by a couple of weeks), has been attributed partly to the lower death risk of the younger (working and socialising) community whose infections are driving the figures. This has been even more noticeable as students have been returning to University.

The following chart from the BBC sourced from PHE data identifies that the caseload in the under-20s comprises predominantly teenagers rather than children of primary school age.

Age-specific IFR estimates
Confirmed Coronavirus cases in England by age group, late August 2020

This has persuaded some to suggest that, rather than the postulated restrictions on everyone, older and more vulnerable people might shield themselves (in effect on a segregated basis) while younger people are more free to mingle. Even some of the older community are suggesting this. To me, that is “turkeys voting for Christmas” (you read it here first, even before the first Christmas jingles on TV ads!)

Not all older or more vulnerable people can, or want to segregate to that extent, and hitherto politicians have tended not to want to discriminate the current interventions in that way.

Scientists, of course, have looked at this, and I add the following by Adam Kucharski (of the modelling team at the London School of Hygiene and Tropical Medicine, and whose opinions I respect as well thought-out) who presents the following chart in a recent tweet, from a paper authored by himself and others from several Universities about social mixing matrices, those Universities including Cambridge, Harvard and London.

Adam presents this chart, saying “For context, here’s data on pre-COVID social contacts between different age groups in UK outside home/work/school (from: https://medrxiv.org/content/10.1101/2020.02.16.20023754v2…). Dashed box shows over 65s reporting contacts with under 65s.

Contact mixing between age groups calibrated by contacting and contacted age groups
Contact mixing between age groups calibrated by contacting and contacted age groups

Adam further narrates this chart in a linked series of tweets on Twitter thus:

I’m seeing more and more suggestions that groups at low risk of COVID-19 should go back to normal while high risk groups are protected. What would the logical implications of this be?

First, let’s pick an example definition of risk. If we use infection fatality risk alone for simplicity (which of course isn’t only measure of severity), there is a clear age pattern, which rises above ~0.1% around age 50 and above ~1% around age 70 (https://medrxiv.org/content/10.1101/2020.08.24.20180851v1…)

Age-specific IFR estimates
Age-specific IFR estimates

Suppose hypothetically we define the over 65 age group as ‘high risk’. That’s about 18% of the UK population, and doesn’t include others with health conditions that put them at more at risk of severe COVID.

The question, therefore, would be how to prevent any large outbreak among ‘low risk’ groups from spreading into ‘high risk’ ones without shutting these risk groups out of society for several months or more (if that were even feasible).

There have been attempts to have ‘shielding’ of risk groups (either explicitly or implicitly) in many countries. But large epidemics have still tended to result in infection in these groups, because not all transmission routes were prevented.

So in this hypothetical example, how to prevent contacts in the box from spreading infection into the over 65s? Removing interactions in that box would be removing a large part of people’s lives, but could the contacts be made less risky?

One option would be to use rapid testing to make sure that these contacts are not infectious, e.g. testing attendees ahead of events/venues/gatherings. But remember, 18% of population are over 65, so that’s a lot of (low risk) contacts who would need to be tested regularly.

Then there’s the question of what happens if contacts are positive… Would they need to self-isolate? People might well do anyway if they knew they’re infected, which could reduce wider transmission…

Depending on what % of population is defined as at high risk, and how many contacts are tested regularly and isolate, could well get a situation where measures reduce transmission in the low risk groups too, leading to a low reproduction number.

If this were to happen, it may become equivalent to a light-touch suppression approach via mass testing: https://twitter.com/AdamJKucharski/status/1303245754853658624?s=20…

It wouldn’t be the first example of a situation where we start with two different approaches but end up with similar outcomes: https://twitter.com/AdamJKucharski/status/1292861098971070467?s=20…

This thread obviously just picks a hypothetical example. But hopefully it shows it’s important to explore the logical implications of a particular scenario, because it won’t necessarily lead where we might initially assume.

I have presented that thread pretty much verbatim (well, after all, I can’t deny a vested interest!) to indicate the complexity of the considerations.

My own opinion is that it isn’t obviously feasible to isolate age-related parts of the community that way – speaking for myself, my own household spans such age groups.

Concluding comments

I support the temporary lockdown, learning the lessons from it and the moves to adjust it (downwards and upwards as judged necessary from sensible forecasts), drawing a balance between the nation’s health and the economic impacts, and I have no time for anything that smacks of anti-vaxxer or conspiracy theories, and anything that might encourage such crackpot ideas.

I’m afraid to say that some of the forecasts published on Twitter, and elsewhere, even by some well-qualified scientists who should know better (and presumably who have their own reasons for doing it – ambition, fame, politics…) do tend to encourage those with such opinions, and I’m very glad to see them called out. References available on application.

Added to the politicising, and subsequent refuting of simple precautions such as face-coverings and social distancing, one of the most dangerous tendencies (in the USA at least, but possibly on the increase here in the UK) is from those who say they won’t take a vaccine when available.

The current UK intervention measures are to be enhanced from tomorrow, September 23rd, following announcements today, as I write this post, and I will update the post to reflect a forecasting analysis including those announced changes.

Categories
Alex de Visscher Coronavirus Covid-19 Superspreader Worldometers

SARS-Cov-2 modelling situation report

Introduction

As we start September, the UK situation regarding Covid-19 cases and deaths has changed somewhat.

Since the UK Government re-assessed the way deaths data is collected and reported, the reported daily deaths resulting from Covid-19 infections have (thankfully) reduced to a very low level, as we see from the UK Government Covid-19 reporting website.

Cases, however, as we see from the Government chart on the right, have started to rise again, although for a number of reasons the impact on deaths has been less than before. Note that this chart plots people testing Covid-19 positive (daily and total to date) against time.

I have integrated this real-world UK reported data with my model data to assess what is happening.

Reporting changes for UK deaths

As I reported in my August 17th post, reported daily deaths in England had previously set no time limit between an individual’s positive test for Covid-19, and when that person died.

The three other home countries in the UK had already been applying a 28-day limit for this interval. It was felt that, for England, this lack of a limit on the time interval 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 the positive test had occurred.

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.

Case numbers and antibody testing

You can see from the following Chart 10 that the plateau for modelled cases is of the order of 3 million. This startling view is supported by a recent Imperial College antibody study reported by U.K. Government here.

I have applied a factor of 8.3 to the reported cases in Chart 10 to bring them into line with the modelled cases, owing to significant under-reporting of the number of UK cases (based on positive Covid-19 tests).

Modelled Cases & Deaths development since Feb 1st - Uninfected, Cumulative Deaths, Uninfected & Seriously Sick
Modelled Cases & Deaths development since Feb 1st – Uninfected, Cumulative Deaths, Uninfected & Seriously Sick

The reported cases (defined, as above, by UK Government as people who have had a positive Covid-19 test) are just 337,168 as at September 1st, as we see from the following chart 9.

Modelled vs Reported Compartment development - Uninfected, Cumulative Cases & Deaths. Modelled Uninfected, All Infected & Seriously Sick
Modelled vs Reported Compartment development – Uninfected, Cumulative Cases & Deaths. Modelled Uninfected, All Infected & Seriously Sick

Testing, antibodies and case counting

The four pillars of Covid-19 testing include a single pillar of antibody testing, although it isn’t clear exactly which class of antibody is being tested. Not all antibody tests are the same.

It is also the case that despite more than 16 million Covid-19 tests having been processed in the UK to date (September 1st), the great majority of people have never been tested.

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.

Even my modelled cases are likely to be a little under-estimated, and some update to my model’s calculation of cases will be made shortly.

Quite apart from the definition and counting of cases, according to a recent report by The Times, referencing this article from the BMJ, results obtained from some antibody testing might well be under-estimated too.

Stephen Burgess, from the Medical Research Council Biostatistics Unit at Cambridge University, and one of the authors, said. “It’s possible that somebody could have antibodies present in their saliva but not in their blood and it’s possible that somebody could have one class of antibody but not another class of antibodies.”

In particular, most antibody tests do not look for a type of response called IgA antibodies, which are made in mucus — in the mouth, eyes and nose. “In certain respiratory diseases, it’s well-documented that it’s possible to beat the infection with an IgA response,” he said.

When scientists have tested for IgA as well as the standard IgG antibodies, they have on occasions found hugely different results. In Luxembourg, IgA were found in 11 per cent of people compared with 2 per cent who tested positive using more conventional tests.

Dr Burgess said that calibrating tests using people who had been more severely ill may mean that a lot of asymptomatic infections are being missed.

The full report is here.

The Times concludes that it’s possible that herd immunity is closer than we think, with regional variations.

Reported Cases and Deaths

The following slide presentation shows only reported data for the UK. With Tom Sutton’s help, I have managed to link his previously developed Worldometers scraping code, which interrogates the daily updated Worldometers site for the UK, to retrieve reported cases and deaths data, to populate my MatLab/Octave model for Coronavirus (originally developed by Prof Alex de Visscher at Concordia University, Montreal).

This allows me to plot both modelled forecast data and reported data on the same charts, plotted from from the Octave forecasting model.

  • Reported UK Deaths vs.Cases since Feb 15th 2020, log chart
  • Reported UK Deaths vs.Cases since Feb 15th 2020, linear chart
  • Reported UK Deaths since Feb 15th 2020, linear chart
  • Reported UK Cases and Deaths since Feb 15th 2020, dual axis, log deaths, linear cases
  • Reported UK Cases and Deaths since Feb 15th 2020, linear dual-axis chart
  • Reported UK Cases and Deaths since Feb 15th 2020, log chart

Chart 3 shows reported deaths plotted against cases, on a log chart, and shows the log curve for deaths flattening as cumulative cases (on the linear x-axis) increase over time, indicating that the ratio of deaths/cases is reducing. This can also be seen very clearly on the linear scaled Chart 4.

Chart 5 shows cumulative deaths over time on linear axes, exhibiting the typical S-curve for infectious diseases; as of September 1st, daily deaths in the UK are in single figures.

Chart 6 shows deaths on a log y-axis (left) and cases on a linear y-axis (right).

Chart 7 plots both deaths and cases on linear y-axes (left and right respectively) for more direct comparison, and again we see that recently, since about Day 110 ( June 1st), cases have increased proportionately much faster than deaths. This date is fairly close to the time that the UK started to ease its lockdown restrictions.

Finally, Chart 8, plotting both deaths and cases on the same log y-axis, shows the relative progression over nearly 200 days since the onset of the pandemic.

These different views clearly show the recent changes in the way the epidemic is playing out in the UK population. Bear in mind that reported cases need something like a factor of 10 applied to bring them to a realistic figure.

Evidence for the under-estimation of Cases

The Imperial College antibody study referenced above 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 forecasted case numbers, relative to the forecasted number of deaths, would be 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. See the World Health Organisation (WHO) description of CFR & IFR here.

In broad terms, my model forecast of c. 42,000 deaths and up to 3 million cases would be a ratio of about 1.4%, and so the IFR relationship between the deaths and cases numbers in my charts seems reasonable.

(NB since we know that the risk of death from Covid-19 is higher in older people, and the age profile of cruise ship passengers is probably higher than average, the Diamond Princess percentages are at the high end of the spectrum.)

Reasons for the reducing deaths/cases ratio

Reported deaths per case are reducing significantly, because:

a) we are more aware of taking care of older people in Care Homes (and certainly not knowingly sending Covid-19 positive old folks to them), sadly lacking in the early days of the pandemic in many countries;

b) relatively more young people are being infected as compared with older people because they are the ones working and going out more, and they have lower mortality than older people;

c) we have some better experience and palliative treatments to help some people recover (eg Dexamethasone as described at https://www.sps.nhs.uk/articles/summary-of-covid-19-medicines-guidance-critical-care/); and

d) daily cases are increasing, rather than reducing, as deaths are.

This is covered in a very good article by Rowland Manthorpe, technology correspondent, and Isla Glaister, data editor of Sky News, whose reports I have read before. The article makes very clear the changes in the age-profile of cases from early March to the end of July.

UK weekly confirmed cases by age, published by Sky September 2nd 2020
UK weekly confirmed cases by age, published by Sky September 2nd 2020

Another view of this is from The Times on September 5th, data sourced from Public Health England (PHE);

UK weekly confirmed cases by age, published by The Times September 5th 2020
UK weekly confirmed cases by age, published by The Times September 5th 2020

and, more specifically, here is how the proportion of cases has shifted between under 40s and over 50s from March until September.

Changing age profile of Covid-19 cases, published by The Times September 6th
Changing age profile of Covid-19 cases, published by The Times September 6th

Issues for modelling presented by local spikes

Modelling the epidemic for the UK is now really difficult, as most cases having an impact on the UK national statistics are nearly all caused by local outbreaks, or spikes – what I call multiple super-spreader events. Although that isn’t quite the right description, these are being caused by behaviour such as lack of social distancing, and maybe erratic mask-wearing on flights returning to the UK with pre- and even post-diagnostic cases on board.

The super-spreader events in the early days in Italy (and in the UK) were caused by people, unknowingly and asymptomatically infected, returning to their home countries from overseas and infecting others.

The increasingly frequent recent events we are seeing are caused, it seems to me, by people who ought, nowadays, to have more awareness of the risks, and know better, compared to those in the early days.

What would be needed to model such events is good local data for each one, and some kind of model for how, when and how often, statistically, these events might occur (aircraft, pubs, clubs, demonstrations, illegal raves and all the rest). Possibly even religious gatherings and other such cultural (including sporting) gatherings have a role.

So modelling this bottom-up is difficult – but feasible, hopefully. In any case, what is needed at the moment is a time-dependent way of handling the infection risks, in the context of these events, the way that lockdown easing points have been introduced to the model.

Worldometers/IHME forecasts and charts

I might say that modelling only by curve fitting, top-down, is pretty incomplete in my view. Phenomenological methods forecast the future based on the past with no ability to model or reflect changes in intervention methods, public behaviour and responses; and I see no capability in the methodology to take super-spreader events into account.

This might be difficult for bottom-up mechanistic modelling, but it’s impossible for broad, country-based curve-fitting, as no link can be made from input changes in government measures, population responses and individual behaviour, to their influence on outcomes.

I covered the comparative phenomenological and mechanistic methods in my previous posts on July 14th and July 18th.

In the charts that follow, we see that forecasts are made for three scenarios: current projections; mandates easing; and universal masks.

To do this, as IHME (Institute for Health Metrics and Evaluation at the University of Washington, USA) say at the IHME FAQ (Frequently Asked Questions) page, Worldometers/IHME forecasts rely on both statistical and disease transmission models: “Our current model is not a disease transmission model. It is a hybrid model that combines both a statistical modeling approach and a disease transmission approach, leveraging the strengths of both types of models, and scaling the results of the disease transmission model to the results of the statistical model.

This enables them to calibrate outcomes based on three outbreak management scenarios.

Illustrating the point, I show the IHME forecast for the UK, followed by that for the USA . First the UK:

Worldometers forecast for the UK, with three scenarios and error bounds

It seems that IHME forecasts for the UK, linked to the Worldometers UK site, are based on a broader view of UK deaths, relating to those where Covid-19 is mentioned on the death certificate, as defined by the UK Office for National Statistics (ONS), but not necessarily cited as the cause of death.

This is even though the Worldometers current reporting charts themselves are consistent with UK Government reported data, which presents deaths in all settings (including hospitals, care homes and the community) but only when Covid-19 is cited as the cause of death.

These ONS and IHME numbers are higher than the UK Government (and Worldometers) statistic. The daily numbers I have been using, presented by the UK Government, continue to be based on the narrower definition – Covid-19 as the cause of death on the death certificate.

Nevertheless, my main point here isn’t about the absolute numbers, but about the forecasting scenarios. We can see that the IHME methodology allows for several forecasting scenarios – current projections based on the interventions currently in place; mandates easing; and universal mask-wearing.

The US IHME forecast is presented similarly:

Worldometers forecast for the USA, with three scenarios and error bounds

In the case of the USA, the numbers are far larger for a much bigger population, and at worst the numbers are staggering. The Covid-19 deaths, currently 187,770 on this chart, had already exceeded Michael Levitt’s well-publicised curve-fitting Twitter forecast made in mid-July, indicating that by August 25th the USA excess deaths will have reduced to a very low level, and that the USA experience of the pandemic would essentially be over, with 170,000 deaths. It seems he agrees that forecast, or at least the way he expressed it, was a mistake.

In the USA case, the numbers are far larger for a much bigger population, and at worst the numbers are staggering. The current 187,770 already exceeds Michael Levitt's well-known curve-fitting forecast made a month ago, indicating that by August 25th the USA excess deaths will have reduced to a very low level, and that the USA experience of the pandemic would essentially be over, with 170,000 deaths. It seems he agrees that forecast, or at least the way he expressed it, was a mistake.
Michael Levitt’s well-publicised curve-fitting Twitter forecast made in mid-July, indicating that by August 25th the USA excess deaths will have reduced to a very low level, and that the USA experience of the pandemic would essentially be over, with 170,000 deaths
Michael Levitt's statement that his estimate of 170,000 reported deaths made 11 July was 7K too low.
Michael Levitt’s statement that his estimate of 170,000 reported deaths made on 11th July was 7K too low.

See Michael’s new UnHerd interview with Freddie Sayers.

As for excess deaths, no measure is without its issues, and the problem there is that Covid-19 deaths will probably have replaced deaths from some other causes (people go out less, so there will be less road accident deaths, for example).

This means that excess deaths reducing to zero isn’t by any means a sufficient test that the SARS-Cov-2 pandemic is all over bar the shouting.

IHME can predict several scenarios, as for the UK, and at best they are predicting 288,381 deaths by the end of the year for the USA. At worst their number is over 600,000. I’m sure things wouldn’t be allowed to get to that.

But these kinds of scenarios for different potential interventions, in combinations, or when eased, just aren’t going to work with curve-fitting alone, where, given just 3 (or at best, 4) parameters to do a least-squares fit of a Cycloid, Gompertz or more general Richards / General Logistics curve to the reported data, any changes to Government interventions and/or public response (even nationally, let alone for local spikes) can’t be reflected. It’s a top-down view of reported data (however well-cleansed) not a bottom-up causation model with the ability to make variations to strategies for intervention.

Mechanistic modelling is hard to do, takes longer and is more expensive in computer time (especially when trying to cover many countries individually); that is where a broader helicopter top-down view from curve-fitting can help to get started. But curve-fitting is not an actionable model for deciding between intervention methods.

I covered these methods in my blog posts on July 14th and July 18th as I was sanity checking my own outlook on modelling methods as between mechanistic modelling (the broad type of the model I use) and phenomenological / statistical methods.

The Imperial College resources

As I have already reported in my blog post on July 18th, Imperial College (and others such as The London School of Hygiene and Tropical Medicine) use a variety of model types and data sources (as do IHME) spanning both mechanistic and statistical methods (which include phenomenological techniques) for forecasts at different levels of detail and over different periods. These are described at the Imperial College’s Medical Research Council MRC Global Infectious Disease Analysis website, where this chart is presented, describing their different methods:

COVID-19 planning tools
Epidemiological models use a combination of mechanistic and statistical approaches.

and they go on to describe the key characteristics of the approaches:

Mechanistic model: Explicitly accounts for the underlying mechanisms of diseases transmission and attempt to identify the drivers of transmissibility. Rely on more assumptions about the disease dynamics.

Statistical model: Do not explicitly model the mechanism of transmission. Infer trends in either transmissibility or deaths from patterns in the data. Rely on fewer assumptions about the disease dynamics.

Mechanistic models can provide nuanced insights into severity and transmission but require specification of parameters – all of which have underlying uncertainty. Statistical models typically have fewer parameters. Uncertainty is therefore easier to propagate in these models. However, they cannot then inform questions about underlying mechanisms of spread and severity.

The forecasts they have made, as you can see, just as the IHME forecasts do, rely on several methodologies.

The table I have shown before from the pivotal Imperial College modelling team March 16th paper:

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)

shows the capability to model a range of Non Pharmaceutical Interventions (NPIs) alone or in different combinations to arrive at forecasts based on such strategies. I covered the NPI variations in some detail in my August 14th blog post, and the mechanistic, statistical and phenomenological approaches in my July 14th blog post and July 18th post.

Discussion

My UK model is tracking quite well after a small change in intervention effectiveness since March 23rd to reflect the retroactive August 12th Government changes in counting deaths, and a slight easing of lockdown on day 105 (May 17th). We see a lot happening here and in other countries, with travel restrictions and quarantining measures changing all the time. It is unlikely that countries will revert to large scale lockdowns.

This is partly because lockdown is seen by many to have done its job; partly because of its negative economic and social impacts; and partly because we know more about the effects of the individual interventions available. Mechanistic modelling methods help discriminate between the effects of the different interventions.

One of the key factors in the choice of interventions is on the basis of longer-term outcomes – the effect of actions taken today on future “herd” immunity of the population, which I covered in my July 31st blog post.

I mention again the influential March 16th Imperial College paper in this respect which, while published nearly 6 months ago, does give an insight into the complexity and capability of modelling methods and data sources and intervention discrimination available to Government advisers.

Modelling on an overall national basis will need some enhancement to cope with the large number of local “spikes” and other events that we have been seeing recently.

Concluding comments

There are reasons for concern – the possibility that current spikes in cases might lead to a major “wave” in the epidemic; that autumn isn’t too far away; and that influenza and other related diseases such as SARS-Cov-2 are more prevalent in the autumn/winter months.

The BBC have reported that the return of students to Universities in the UK is expected to lead to a high risk of increasing the rate of Covid-19 cases. We will see.

I leave it to the Sky News summary to express closing thoughts, and some optimism.

The fear among government scientists is that if the outbreak gets out of control among young people, it will eventually leak into the more vulnerable parts of the population. What might look like a divergence between cases and deaths is actually just a larger lag. To find the answer to that, the best places to look are France and Spain, where cases are rising fast, but deaths and hospitalisations are still low. But whatever happens, we should remember: this isn’t March all over again. We test so much more. We know so much more about treatment. And we all understand how to change our behaviour. That is cause for optimism as we face the next six months.