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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.

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.