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Adam Kucharski Alex de Visscher Coronavirus Covid-19 David Spiegelhalter Superspreader Worldometers

Model updates for UK lockdown easing points

Introduction

As I reported in my previous post on 31st July, the model I use, originally authored by Prof. Alex de Visscher at Concordia University in Montreal, and described here, required an update to handle several phases of lockdown easing, and I’m glad to say that is now done.

Alex has been kind enough to send me an updated model code, adopting a method I had been considering myself, introducing an array of dates and intervention effectiveness parameters.

I have been able to add the recent UK Government relaxation dates, and the estimated effectiveness of each into the new model code. I ran some sensitivities which are also reported.

Updated interventions effectiveness and dates

Now that the model can reflect the timing and impact of various interventions and relaxations, I can use the epidemic history to date to calibrate the model against both the initial lockdown on March 23rd, and the relaxations we have seen so far.

Both the UK population (informally) and the Government (formally) are making adjustments to their actions in the light of the threats, actual and perceived, and so the intervention effects will vary.

Model adjustments

At present I am experimenting with different effectiveness percentages relating to four principal lockdown relaxation dates, as described at the Institute for Government website.

In the model, the variable k11 is the starting % infection rate per day per person for SARS-Cov-2, at 0.39, which corresponds to 1 infection every 1/0.39 days ~= 2.5 days per infection.

Successive resetting of the interv_success % model variable allows the lockdown, and its successive easings to be defined in the model. 83.5% (on March 23rd for the initial lockdown) corresponds to k11 x 16.5% as the new infection rate under the initial lockdown, for example.

In the table below, I have also added alternative lockdown easing adjustments in red to show, by comparison, the effect of the forecast, and hence how difficult it will be for a while to assess the impact of the lockdown easings, volatile and variable as they seem to be.

DateDay Steps and example measuresChanges to % effectiveness
23rd March52Lockdown starts+83.5%
13th May105Step 1 – Partial return to work
Those who can work from home should do so, but those who cannot should return to work with social distancing guidance in place. Some sports facilities open.
-1% = 82.5%

-4% = 79.5%
1st June122Step 2 – Some Reception, Year 1 and Year 6 returned to school. People can leave the house for any reason (not overnight). Outdoor markets and car showrooms opened.-5% = 77.5%

-8% = 71.5%
15th June136Step 2 additional – Secondary schools partially reopened for years 10 and 12. All other retail are permitted to re-open with social distancing measures in place.-10% = 67.5%

+10% = 81.5%
4th July155Step 3 – Food service providers, pubs and some leisure facilities are permitted to open, as long as they are able to enact social distancing.+20% = 87.5%

-6% = 75.5%
1st August186Step 3 additional – Shielding for 2m vulnerable people in the UK ceases0% = 87.5%
Dates, examples of measures, and % lockdown effectiveness changes on k11

After the first of these interventions, the 83.5% effectiveness for the original March 23rd lockdown, my model presented a good forecast up until lockdown easing began to happen (both informally and also though Government measures) on May 13th, when Step 1 started, as shown above and in more detail at the Institute for Government website.

Within each easing step, there were several intervention relaxations across different areas of people’s working and personal lives, and I have shown two of the Step 2 components on June 1st and June 15th above.

I applied a further easing % for June 15th (when more Step 2 adjustments were made), and, following Step 3 on July 4th, and the end (for the time being) of shielding for 2m vulnerable people on August 1st, I am expecting another change in mid-August.

I have managed to match the reported data so far with the settings above, noting that even though the July 4th Step 3 was a relaxation, the model matches reported data better when the overall lockdown effectiveness at that time is increased. I expect to adjust this soon to a more realistic assessment of what we are seeing across the UK.

With the % settings in red, the outlook is a little different, and I will show the charts for these a little later in the post

The settings have to reflect not only the various Step relaxation measures themselves, but also Government guidelines, the cumulative changes in public behaviour, and the virus response at any given time.

For example, the wearing of face coverings has become much more common, as mandated in some circumstances but done voluntarily elsewhere by many.

Comparative model charts

The following charts show the resulting changes for the initial easing settings. The first two show the new period of calibration I have used from early March to the present day, August 4th.

On chart 4, on the left, you can see the “uptick” beginning to start, and the model line isn’t far from the 7-day trend line of reported numbers at present (although as of early August possibly falling behind the reported trend a little).

On the linear axis chart 13, on the right, the reported and model curves are far closer than in the version in my most recent post on July 31st, when I showed the effects of lockdown easing on the previous forecasts, and I highlighted the difficulty of updating without a way of parametrising the lockdown easing steps (at that time).

Using the new model capabilities, I have now been able to calibrate the model to the present day, both achieving the good match I already had from March 23rd lockdown to mid-May, and then separately to adjust and calibrate the model behaviour since mid-May to the present day, by adjusting the lockdown effectiveness at May 15th, June 1st, June 15th and July 4th, as described earlier.

The orange dots (the daily deaths) on chart 4 tend to cluster in groups of 4 or 5 per week above the trend line (and also the model line), and 3 or 2 per week below. This is because of the poor accuracy of some reporting at weekends (consistently under-reporting at weekends and recovering by over-reporting early the following week).

The red 7-day trend line on chart 4 reflects the weekly average position.

Looking a little further ahead, to September 30th, this model, with the initial easing settings, predicts the following behaviour, prior to any further lockdown easing adjustments, expected in mid-August.

Chart 12 for the comparison of cumulative & daily reported & modelled deaths, on the basis of 83.5% effectiveness, modified in 4 steps by -1%, -5% -10% and +2% successively
Chart 12 for the comparison of cumulative & daily reported & modelled deaths

Finally, for comparison, the Worldometers UK site has a link to its own forecast site, which has several forecasts depending on assumptions made about mask-wearing, and/or continued mandated lockdown measures, with confidence limits. I have screenshot the forecast on October 1st, where it shows 48,268 deaths assuming current mandates continuing, and mask-wearing.

My own forecast shows 47,201 cumulative deaths at that date.

Worldometers forecasts on the basis of mask wearing vs. no mandated measures, with confidence limits
Worldometers forecasts on the basis of mask wearing vs. no mandated measures, with confidence limits

Alternative % settings in red

I now present a slideshow of the corresponding charts with the red % easing settings. The results here are for the same initial lockdown effectiveness, 83.5%, but with successive easings at -4%, -8%, +10% and -6%, where negative is relaxation, and positive is an increase in intervention effectiveness.

  • Chart 12 for the comparison of cumulative & daily reported & modelled deaths to 26th April 2021, on the basis of 83.5% effectiveness, modified in 4 steps by -4%, -8% +10% and -6%% successively
  • Chart 12 for the comparison of cumulative & daily reported & modelled deaths to 30th Sep 2020, , on the basis of 83.5% effectiveness, modified in 4 steps by -4%, -8% +10% and -6%% successively
  • Chart 4 for the comparison of cumulative & daily reported & modelled deaths, plus reported trend line, on the basis of 83.5% effectiveness
  • Model forecast for the UK deaths as at August 8th, compared with reported for 83.5% lockdown effectiveness
  • Model forecast (linear axes) for the UK deaths as at August 8th, compared with reported for 83.5% lockdown effectiveness, modified in 4 steps by -4%, -8% +10% and -6%% successively

The model forecast here for September 30th is for 49, 549 deaths, and the outlook for the longer term, April 2020, is for 52,544.

Thus the next crucial few months, as the UK adjusts its methods for interventions to be more local and immediate, will be vital in its impact on outcomes. The modelling of how this will work is far more difficult, therefore, with fine-grained data required on virus characteristics, population movement, the comparative effect of different intervention measures, and individual responses and behaviour.

Hotspots and local lockdowns

At present, because the UK reported case number trend has flattened out and isn’t decreasing as fast, and because of some local hotspots of Covid-19 cases, the UK Government has been forced to take some local measures, for example in Leicester a month ago, and more recently in Manchester; the scope and scale of any lockdown adjustments is, therefore, a moveable target.

I would expect this to be the pattern for the future, rather than national lockdowns. The work of Adam Kucharski, reported at the Wellcome Open Research website, highlighting the “k-number”, representing the variation, or dispersion in R, the reproduction number, as he says in his Twitter thread, will be an important area to understand.

The k-number might well be more indicative, at this local hotspot stage of the crisis, than just the R reproduction number alone; it has a relationship to the “superspreader” phenomenon discussed for SARS in this 2005 paper, that was also noticed very early on for SARS-Cov-2 in the 2020 pandemic, both in Italy and also in the UK. I will look at that in more detail in another posting.

Superspreading relates to individuals who are infected (probably asymptomatically or pre-symptomatically) who infect others in a closed social space (eg in a ski resort chalet as reported by the BBC on February 8th) without realising it.

The hotspots we are now seeing in many places might well be related to this type of dispersion. The modelling for this would be a further complication, potentially requiring a more detailed spatial model, which I briefly discussed in my blog post on modelling methods on July 14th.

Superspreading might also need to be understood in relation to the opening of schools, in August and September (across the four UK home countries). It might have been a factor in the Israel experience of return to schools, as covered by the Irish Times on August 4th.

The excess deaths measure

There has been quite a debate on excess deaths (often a seasonal comparison of age-related deaths statistics compared with the previous 5 years) as a measure of the overall position at any time. As I said in a previous post on June 2nd, this measure does mitigate any arguments as to what is a Covid-19 fatality, and what isn’t.

The excess deaths measure, however, has its own issues with regard to the epidemic’s indirect influence on the death rates from other causes, both upwards and downwards.

Since there is less travel (on the roads, for example, with fewer accidents), and many people are taking more care in other ways in their daily lives, deaths from some other causes might tend to reduce.

On the other hand, people are feeling other pressures on their daily lives, affecting their mood and health (for example the weight gain issues reported by the COVID Symptom Study), and some are not seeking medical help as readily as they might have done in other circumstances. Both factors tend to increase illness and potentially death rates.

Even as excess deaths reduce, then, it may well be that Covid-19 deaths increase as others reduce. Possibly a crossover with seasonal influenza deaths, later on, might be masked by the overall excess deaths measure.

As I also mentioned in my post on July 6th, deaths in later years from other causes might increase because of this lack of timely diagnosis and treatment for other “dread” diseases, as, for example, for cancer, as stated by Data-can.org.uk.

So no measure of the epidemic’s effects is without its issues. Prof. Sir David Spiegelhalter covered this aspect in a newspaper article this week.

Discussion

The statistical interpretation and modelling of data related to the pandemic is a matter of much debate. Some commentators and modellers are proponents of quite different methods of data recording, analysis and forecasting, and I covered phenomenological methods compared with mechanistic (SIR) modelling in previous posts on July 14th and July 18th.

The current reduced rate of decline in cases and deaths in some countries and regions, with concomitant local outbreaks being handled by local intervention measures, including, in effect, local lockdowns, has complicated the predictions of some who think (and have predicted) that the SARS-Cov-2 crisis will soon be over (some possibly for political reasons, some of them scientists).

Even when excess deaths reduce to zero, this doesn’t mean that Covid-19 is over, because, as I mentioned above, illness and deaths from other causes might have reduced, with Covid-19 filling the gap.

There are also concerns that recovery from Covid-19 as a death threat can be followed by longer-lasting illness and symptoms, and some studies (for example this NHLBI one) are gathering evidence, such as that covered by this report in the Thailand Medical News.

This Discharge advice from the UK NHS makes continuing care requirements for discharged Covid-19 patients in the UK very clear.

It is by no means certain, either, that recovery from Covid-19 confers immunity to SARS-Cov-2, and, if it does, for how long.

Concluding comments

I remain of the view that in the absence of a vaccine, or a very effective pharmaceutical treatment therapy, we will be living with SARS-Cov-2 for a long time, and that we do have to continue to be cautious, even (or, rather, especially) as the UK Government (and many others) move to easing national lockdown, at the same time as being forced to enhance some local intervention measures.

The virus remains with us, and Government interventions are changing very fast. Face coverings, post-travel quarantining, office/home working and social distancing decisions, guidance and responses are all moving quite quickly, not necessarily just nationally, but regionally and locally too.

I will continue to sharpen the focus of my own model; I suspect that there will be many revisions and that any forecasts are now being made (including by me) against a moving target in a changing context.

Any forecast, in any country, that it will be all over bar the shouting this summer is at best a hostage to fortune, and, at worst, irresponsible. My own model still requires tuning; in any case, however, I would not be axiomatic about its outputs.

This is an opinion informed by my studies of others’ work, my own modelling, and considerations made while writing my 30 posts on this topic since late March.

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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.

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Coronavirus Covid-19 Worldometers

Coronavirus modelling update

Introduction

In my previous post on June 28th, I covered the USA vs. Europe Coronavirus pandemic situations; herd immunity, and the effects of various interventions on it, particularly as envisioned by the Imperial College Covid-19 response team; and the current forecasts for cases and deaths in the UK.

I have now updated the forecasts, as it was apparent that during the month of June, there had been a slight increase in the forecast for UK deaths. Worldometers’ forecast had increased, and also the reported UK numbers were now edging above the forecast in my own model, which had been tracking well as a forecast (if very slightly pessimistically) until the beginning of June.

This might be owing both to informal public relaxation of lockdown behaviour, and also to formal UK Government relaxations in some intervention measures since the end of May.

Re-forecast

I have now reforecast my model with a slightly lower intervention effectiveness (83% instead of 83.5% since lockdown on 23rd March), and, while still slightly below reported numbers, it is nearly on track (although with the reporting inaccuracy each weekend, it’s not practical to try to track every change).

My long term outlook for deaths is now for 46,421 instead of 44,397, still below the Worldometers number (which has increased to 47,924 from 43,962).

Here are the comparative charts – first, the reported deaths (the orange curve) vs. modelled deaths (the blue curve), linear axes, as of July 6th.

Comparing this pair of charts, we see that the .5% reduction in lockdown intervention effectiveness (from March 23rd) brings the forecast, the blue curve on the left chart, above the reported orange curve. On the right, the forecast, which had been tracking the reported numbers for a month or more, had started to lag the reported numbers since the beginning of June.

I present below both cumulative and daily numbers of deaths, reported vs. forecast, with log y-axis. The scatter in the daily reported numbers (orange dots) is because of inconsistencies in reporting at weekends, recovered during each following week.

In this second pair of charts, we can just see that the rate of decline in daily deaths, going forward, is slightly reduced in the 83% chart on the left, compared with the 83.5% on the right.

This means that the projected plateau in modelled deaths, as stated above, is at 46,421 instead of 44,397 in my modelled data from which these charts are drawn.

It also shows that the forecast reduction to single digit (<10) deaths per day is pushed out from 13th August to 20th August, and the forecast rate of fewer than one death per day is delayed from 21st September to 30th September.

ONS & PHE work on trends, and concluding comments

Since the beginning of lockdown relaxations, there has been sharpened scrutiny of the case and death numbers. This monitoring continues with the latest announcements by the UK Government, taking effect from early July (with any accompanying responses to follow from the three UK devolved administrations).

The Office for National Statistics has been monitoring cases and deaths rates, of course, and the flattening of the infections and deaths reductions has been reported in the press recently.

July 3rd Times reporting ONS regarding trends in Covid-19 incidence rates and deaths

As the article says, any movement would firstly be in the daily number of cases, with any potential change in the deaths rate following a couple of weeks after (owing to the Covid-19 disease duration).

Source data for the reported infection rate is on the following ONS chart (Figure 6 on their page), where the latest exploratory modelling, by ONS research partners at the University of Oxford, shows the incidence rate appears to have decreased between mid-May and early June, but has since levelled off.

Figure 6: The latest exploratory modelling shows incidence appears to have decreased between mid-May and early June
Estimated numbers of new infections of the coronavirus (COVID-19), England, based on tests conducted daily since 11 May 2020

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

The ONS is also tracking Excess deaths, and it seems that the Excess deaths in 2020 in England & Wales have reduced to below the five-year average for the second consecutive week.

The figures can be seen in the spreadsheet here, downloaded from the ONS page. The following chart appears there as Figure 1, also showing that the number of deaths involving Covid-19 decreased for the 10th consecutive week.

Number of deaths registered by week, England & Wales, Dec 2019 to 26th June 2020
Number of deaths registered by week, England & Wales, Dec 2019 to 26th June 2020

There are warnings, however, also reported by The Times, that there may be increased mortality from other diseases (such as cancer) into 2021 because worries about the pandemic haves led to changes in patterns of use of the NHS, including GPs, with fewer people risking trips to hospital for diagnosis and/or treatment. The report referred to below from Data-can.org.uk highlights this

I will make any adjustments to the rate of change as we go forward, but thankfully daily numbers are just reducing at the moment in the UK, and I hope that this continues.

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Uncategorized

Coronavirus – possible trajectories

I guess the UK line in the Johns Hopkins chart, reported earlier, might well flatten at some point soon, as some other countries’ lines have.


But if we continue at 3 days for doubling of cases, according to my spreadsheet experiment, we will see over 1m cases after 40 days. See:
https://docs.google.com/spreadsheets/d/1kE_pNRlVaFBeY5DxknPgeK5wmXNeBuyslizpvJmoQDY/edit?usp=sharing
and the example outputs attached for 3, 5 and 7 day doubling.

A million cases by 40 days if we continue on 3 day doubling of cases


If we had experienced (through the social distancing and other precautionary measures) and continue to experience a doubling period of 5 days (not on the chart but a possible input to my spreadsheet), it would lead to 25,000 cases after 40 days.

25600 cases at 5 day doubling since case 100


If we had managed to experience 7 days for doubling of cases (as Japan and Singapore seem to have done), then we would have seen 5000 cases at 40 days (but that’s where we are already, so too late for that outcome).

Not a feasible outcome for the UK, as we are already at 5000 cases or more


So the outcomes are VERY sensitively dependent on the doubling period, which in turn is VERY dependent on the average number of people each carrier infects.


I haven’t modelled that part yet, but, again, assumptions apart, the doubling period would be an outcome of that number, together with how long cases last (before death or recovery) and whether re-infection is possible, likely or frequent. It all gets a bit more difficult to be predictive, rather than mathematically expressing known data.


On a more positive note, there is a report today of the statistical work of Michael Levitt (a proper data scientist!), who predicted on February 21st, with uncanny accuracy, the March 23rd situation in China (improvements compared with the then gloomy other forecasts). See the article attached.

Michael Levitt article from The Times 24th March 2020
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Uncategorized

Coronavirus – forecasting numbers

A few people might have see the Johns Hopkins University Medical School chart on Covid-19 infection rates in different countries. This particular chart (they have produced many different outputs, some of them interactive world incidence models – see https://coronavirus.jhu.edu/map.html for more) usefully compares some various national growth rates with straight lines representing different periods over which the number of cases might double – 1 day, 2 days, 3 days and 7 days. It’s a kind of log chart to base 2.

Johns Hopkins University national trends, log base 2 chart

I’ve been beginning to simulate the outcomes for 2 input data items:

your chosen number of days (x) since the outbreak (defined at 100 cases on day zero to give a base of calculation);

your chosen rate of growth of cases, expressed by an assumed number of days for doubling the cases number (z), and then;

the output, the number of cases (y) on day x.

This spreadsheet allows you , in the last columns, to enter x and z in order to see the outcome, y.

Of course this is only an output model, it knows nothing about the veracity of assumptions – but the numbers (y) get VERY large for small doubling periods (z).

Try it. Only change the x and z numbers, please.

https://docs.google.com/spreadsheets/d/1kE_pNRlVaFBeY5DxknPgeK5wmXNeBuyslizpvJmoQDY/edit?usp=sharing