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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.

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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.