Archive for December, 2020

External Wall Insulation: How well is it working?

December 23, 2020

How well is my External Wall Insulation (EWI) working?

I am so glad you asked. The EWI installation by Be Constructive was completed in November and at this point in the winter, it appears to have reduced gas consumption by “about 50%.”

In this article I will show you the results of my measurements so far and explain how I made this estimate.

You can find previous articles on this topic listed at the end of this article.

Measurement#1: Reading the Gas Meter

In my house, we use a gas boiler for hot water, room-heating via radiators, and for cooking. I have been reading the gas meter weekly for the last two years or so (see graph below) and the strong seasonal variation is associated almost entirely with heating the house in winter.

Gas consumption in KWh per day for the last two years. The data are averaged over 5 weeks to smooth out the noise. The pink boxes show the dates of key interventions which I think affected gas consumption Click for a larger version.

It is pretty clear that this winter I am using considerably less gas than in previous winters. Also we can see a decline in gas consumption after day 660 when the installation of the External Wall Insulation (EWI) began.

To put the scale in context, using 24 kWh per day is equivalent to having a 1 kW heater on for 24 h. So the peak demand of just over 100 kWh/day is equivalent to having a 4.2 kW heater running all day.

But perhaps the lower gas consumption is due to milder weather?

Measurement#2: Reading the External Temperature

To check for this I can plot the temperature ‘demand’ alongside the gas consumption. The demand is shown on the right-hand axis.

In case you haven’t seen these two curves plotted together before, I will just note how strong the correlation is.

With my wife’s consent, I have kept the thermostat location and setting (19 °C) the same for this period. So I plot how many degrees below 19 °C the external weekly temperature falls.

Gas consumption in KWh per day for the last two years as shown above. and average temperature ‘demand’ shown against the right-hand axis. The data are averaged over 5 weeks to smooth out the noise. The pink boxes show the dates of key interventions which I think affected gas consumption Click for a larger version.

This winter the temperature ‘demand’ so far appears to be similar to last winter with average temperatures around 8 °C i.e. 19 – 8 = 11 °C of demand.

But instead of 70 kWh per day of gas, I am using just under 40 kWh/day. So gas consumption appears to be about 43% lower.

However we use around 5 kWh of gas on cooking and water heating even in summer – so the space heating performance appears to be improved from 65 kWh per day to 35 kWh/day, i.e. the gas used for heating directly appears to be about 47% lower.

But the uncertainties on this figure are sufficient that I think “about half” covers it for now. I really need a whole winter of performance to get a better figure.

Thermal Model

Finally I can make a model (– – –) that predicts the gas consumption in terms of the weather, and a parameter that describes the house insulation.

Gas consumption in KWh per day as shown in the first graph, and a model (– – –) which tries to predict gas consumption based on the average temperature ‘demand’ shown in the second graph. The constant of proportionality for the model is changed to allow the model to match the gas consumption in the winters of 2018/19 and 2019/20. The constant for the current winter is based on what I had been hoping for.  Click for a larger version.

The model (– – –) assumes that the gas consumption is composed of two parts.

  • A year-round consumption of 5 kWh per day (equivalent to a continuous 208 W) on cooking and hot-water heating.
  • A weather-dependent part that is proportional to how far below 19 °C the external temperature falls.

The weather-dependent part has a constant of proportionality which describes how much gas power is used for each degree Celsius that the external temperature falls below 19 °C.

In the graph above I have changed the constant of proportionality around Day 250 – when most windows were triple-glazed – and around Day 660 – when the EWI commenced.

  • In the winter of 2018/2019 it took 280 W of continuous power for each 1 °C above the external temperature.
    • This corresponds to 6.7 kWh/day for each 1 °C above the external temperature.
  • In the winter of 2019/2020 it took 240 W of continuous power for each 1 °C above the external temperature.
    • This corresponds to 5.7 kWh/day for each 1 °C above the external temperature.
  • In this winter of 2020/2021 I hoped the EWI would mean I needed only 134 W of continuous power for each 1 °C above the external temperature.
    • This corresponds to 3.2 kWh/day for each 1 °C above the external temperature.

Looking at this winter’s data so far, the actual gas consumption is below the model (– – –) suggesting that the insulation is performing better than expected. The constant of proportionality is probably close to 120 W of continuous power for each 1 °C above the external temperature (or 3.2 kWh/day for each 1 °C above the external temperature).

So how well is my External Wall Insulation (EWI) working?

  • It’s performing roughly how I anticipated.

And so as the year ticks over I will add this project to the small pile of ‘Good things that happened in 2020’.

But I have – unwisely perhaps – been making more measurements – recording temperature and gas consumption day-by-day. And these more detailed measurements have been making me think I might not have understood things fully.

But all that is material for another article.

For now I wish anyone who has read this far, a Happy Christmas and a much improved 2021.

 

Previous articles on this topic

2020

2019

 

Everything is Rubbish!

December 22, 2020

All the factories in all the world are just making rubbish. All that differs is the speed and path of the trajectory from Factory to Dump.

Friends, when I say that “Everything is Rubbish“, this is not the moaning of a 60-year old man dissatisfied with new-fangled ways.

This is the insight of a 60-year old man who has seen with perfect clarity that, with very few exceptions, every object one ever ‘owns’ is really just ‘leased’ as it makes its way from a factory to a dump.

Personally 

Recently I have been sorting my way through a loft filled with the detritus of bringing up two children, along with a few items of memorabilia from earlier in my own life.

And the following thought is irrepressible:

If anyone else looked at this they would call it junk“.

And in a related theme, a couple of close friends have recently been charged with sorting the belongings of a deceased parent.

And items which were one preciously hoarded as treasures, are revealed in the cold light of a parent’s absence to have negative monetary value: they are impossible even to give away.

And in a further related theme, I tried to play a VHS-Video Cassette the other day – and the player would not play. [PAUSE for younger readers to laugh at this folly].

I looked inside and poked around – they really are ingenious! – but to no avail. This package of metal and components is now junk. And so are all the 100 or so video cassettes. In their day I probably paid £1000 for them. Now, all the subtlety and artistry that went into their creation is worth nothing.

What has lasted?

I do have a small number of items which have lasted longer than the average.

  • I have a couple of photographs of my parents’ wedding – these are 68 years old and still in excellent condition.
  • Most days I still use the calculator that I bought in 1978 before I went to University. And I have a few books from that era too.
  • And I still regularly listen to music through  a pair of Wharfedale Denton loudspeakers. These were a present from my father for my 18th birthday in 1978. I recall that he could not believe that a pair of loudspeakers could conceivably cost £55 – but if were he alive today he would be pleased at their longevity.

But even for these items, it is not that they will last forever, but simply that the arc of their trajectory from factory to dump is slightly longer.

Why do I mention this?

Because the truth has struck me hard in the last few weeks.

  • All the factories in the world are really Rubbish Factories

All that differs is the category of rubbish and the arc of its path from Factory to Dump.

I know I am not the first person to mention this.

And I know that my own life is not a good exemplar of a life which minimises the amount of rubbish generated.

But it just struck me as being deeply, deeply true.

 

 

 

 

 

It didn’t have to be this way.

December 21, 2020

If the Government had followed advice and had a lockdown in October which had the same effect as the Lockdown#2 did in November. Then by mid-November 6000 fewer people would have died. Click for a larger image.

Friends. Let me ask you to imagine an alternative reality.

In this reality, our government would have taken the advice of SAGE and instituted Lockdown#2 in October instead of November. It is not a crazy idea that a government should accept the advice of the people it has asked to advise it. Here are some news stories from 13th October 2020.

If they had taken that advice, where would would be now?

Let’s assume that:

  • Events would have evolved along a similar path to what actually happened one month later when we entered Lockdown#2. And that…
  • After the end of Lockdown, things continued as they actually continued.

Based on these assumptions

  • I calculate that in Mid-November 6000 fewer people would have died than had actually died at that point.

Additionally, the death rate would have still been below 100 people per day. At that low rate, there would have been an extended window in which Track Trace and Isolate might conceivably have been made to work.

What would have happened after this is harder to say. Every European country has seen a resurgence in the virus, and so I guess we would have too.

Here are two possibilities.

  • If we had managed to control the virus at low levels, then compared with the situation now, 19,000 people would be alive and we would be able to have Christmas celebrations.
  • If the virus had taken off exactly as it actually did in October – but just delayed by 6 weeks, then the number of people saved would only have been about 13,000.

If the Government had followed advice and had a lockdown in October which had the same effect as the Lockdown#2 did in November. Then to date – 20th December 2020 – somewhere between either 13,000 (red curve) or 19,000 (blue curve) fewer people would have died. Click for a larger image.

Why do I mention this?

This is not complex mathematics.

And while there are uncertainties in this calculation, the number of lives which might have been saved is on the order of 10,000 – no matter how you make the calculation.

The understanding that when a virus is in a period of exponential growth, acting earlier saves lives and livelihoods, is well-known to anyone with even the slightest knowledge of this field.

Even I recognised the trend and recommended a series of planned Lockdowns on 26th September 2020

It seems clear to me that the government must have known what was happening and yet they deliberately chose the path they did knowing full well that thousands of their own compatriots would die.

This is a despicable behaviour and ought to elicit the resignation of the Prime Minister.

Image Stolen from Red Molotov

Expert Scientific Advice

December 19, 2020

At times like this, we would hope that SAGE would be providing us with wise advice and not merely acting to flavour an official Government stuffing.

While I appreciate that SAGE may well be providing good advice to the government – who are then ignoring it – I also fear that SAGE has been ‘captured’ and that its advice is spun. Or worse, that they pre-spin their advice to make it acceptable to government.

In this context we should be grateful to Independent SAGE for very plainly and openly stating the facts as they see them.

In case you have not seen their weekly briefings, I am re-posting this recording of the Independent SAGE meeting yesterday (Friday 18th December 2020).

I found the briefing refreshingly unspun. It is at times critical – indeed very strongly critical – of government failings. But the criticism is because the government has actually failed.

I found it odd after each criticism not to hear the ‘echo’ of a Government Minister “explaining” why – for example – the trail of death caused by the continued failure of Track, Trace and Isolate is in fact not a failure, but indeed a triumph against the odds.

I found the data on the local failure of the Tier system (about 5 minutes in to the initial 10 minute briefing) particularly striking, because this analysis has not been mentioned by – for example – the BBC.

Anyway – it’s there if you want to see how things stand.

COVID-19: Day 352: The Second Wave will be deadlier than the First

December 18, 2020

Summary

Friends: Despite good news on vaccines, the corona virus outlook over the coming month is bleak.

This week the rates of positive tests and  hospital admissions have continued to increase.

Today (Day 353) the seven day rates of positive tests and hospital admissions are higher, and rising faster, than before Lockdown#2 started on Day 310.

Sadly, the second wave is proving more deadly than the first.

  • I have estimated the switchover from First to Second wave as taking place on 16th August (Day 228) – close to date of minimum hospital admissions.
  • If admissions continue at the current value (7-day average of 1700 admissions per day) up to the end of the year – a near certainty –  then the cumulative admissions for the second wave will be equal to the total admissions for the first wave (135,000) later in December.
  • If deaths continue at the current value (7-day average of 430 deaths per day), then the cumulative deaths for the second wave will equal the 41,000 deaths for the first wave sometime in late January 2021.

And of course, the second wave is not over.

Recent data for the number of daily positive tests and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily hospital admissions and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily deaths and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Data from Table 1d of the ONS spreadsheet: Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 12 th December 2020 on average 1.1 % of the UK population were actively infected, up from the previous weeks estimate of 0.9%.

The raw count of positive tests was:

  • 1,672 from 159,052 people tested in the two weeks to 12th December,
  • 1,992 from 184,538 people tested in the preceding two weeks, and
  • 2,096 from 163,077 people tested in the two weeks preceding that.

The data in the table above are graphed below.

ONS Estimated prevalence of COVID-19 in England extracted from Table 1 d Click for a larger version.

Note these estimates come from random survey tests (so-called Pillar 4 tests), not clinical tests.

I have shown two curves on the graph above.

  • The black dotted line (– – –) is the same curve I have plotted for the previous thirteen weeks. (Link)
  • It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
  • The blue continuous curve is the ONS model for what is ‘really happening’.
    • I cannot explain how this estimate lies consistently below the data on which the model is based. Clearly there is something I have still not understood. I did ask ONS but they did not reply.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July. This week I have extend the time frame to look into the first four months of 2021.

Data for positive casesdaily hospital admissions and daily deaths. Click for a larger version. Recent details for each quantity are given in separate graphs at the head of the article.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days – the rate at which the epidemic declined during Lockdown#1.
  • The increasing trends correspond to quantities doubling every 15 days, roughly the rate at which the second wave grew.

Data#3. Details and Projections

Because we are now in the non-exponential phase of the epidemic, I have re-plotted recent data for casesadmissions and deaths on a linear scale: these can be found at the top of the article.

I have also included some projections (as dotted lines) assuming that:

  • The effects of Lockdown#2 began to show through on Day 324,
  • The declines will be as swift as in Lockdown#1 (halving every 21 days).
  • The declines will continue after the 2nd December end of Lockdown#2.
  • The decline in hospital admissions is delayed 5 days with respect to cases
  • The delay in deaths is delayed 7 days (a change from last week) with respect to hospital admissions.

The curved dotted-line projections on the linear graphs at the graphs at the top of this article are effectively the same as the straight-line projections on the combined (logarithmic) graph. Please note that:

  • These are guidelines not predictions.
  • Look to see if quantities fall faster than this, or slower than this.

It is clear that the data are no longer following the hoped-for declining trends.

Since cases lead to admissions which lead to deaths, we can use data for positive cases and  hospital admissions to predict deaths in the coming days and weeks. These projections are shown below.

Data for daily deaths. are shown as a solid black line. The yellow dotted curve (– – –) is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve (– – –) is the predicted daily death curve assuming 2% of cases die after 17 days. Click for a larger version.

The predicted death rate based on positive cases suggested there would be a very large fall in the death rate which has not materialised. My guess is that the drop in positive cases in the last two weeks of lockdown was caused by some kind of sampling variation.

The predictions based on hospital admissions are more reliable (I think) because they are less affected by the ‘fair-sampling’ issues when anticipating deaths from positive cases.

These predictions suggest that in the coming weeks deaths will rise further – approaching 500 deaths per day in the new year.

So…

In my opinion, it’s all a big mess: but you knew that already so I won’t dwell on it.

But with the vaccine being distributed – my 84 year-old father-in-law will receive his first shot tomorrow – we can finally look forward to a reduction in the death rate.

The UK population is about 60 million and herd immunity will not act strongly in our favour until about 60%-70% of people are immunised. So we might expect to see a natural decline in the virus without social distancing after about 40 million people have become immune.

Guessing that 1 million vaccinations per week are possible – I could not find a reliable estimate – then herd immunity will not come until the autumn.

However, there are only 12.5 million people over 60 (link) and these (along with health care workers) are amongst the first in line for the vaccine. It seems just possible that this entire cadre could be immunised by Easter (April 4th).

If that were achieved then hospital admissions and deaths should fall steadily through the early part of 2021 even as positive cases likely continue to rise: something to look forward to.

Stay safe.

COVID-19: Day 338: Here we go again. Again.

December 11, 2020

Summary

Friends: This vale of tiers is becoming a vale of tears.

Last week I said that :

the rates of positive tests and  hospital admissions are clearly declining but the rate of deaths is only showing the first hints of a decline.

Encouragingly, the rates of decline were similar to those seen in Lockdown#1.

This week the rates of positive tests and  hospital admissions have increased and are continuing to increase. As anticipated, there has been a slight fall in the rate of deaths.

Recent data for the number of daily positive tests and their 7-day retrospective average together with last week’s optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily hospital admissions and their 7-day retrospective average together with last week’s optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily deaths and their 7-day retrospective average together with an optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Data from Table 1d of the ONS spreadsheet: Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 5th December 2020 on average 0.90% of the UK population were actively infected, similar to the previous weeks estimate of 0.88%.

The raw count of positive tests was:

  • 1,637 from 171,170 people tested in the two weeks to 5th December,
  • 2,164 from 177,318 people tested in the preceding two weeks, and
  • 1,974 from 158,347  people tested in the two weeks preceding that.

The data in the table above are graphed below.

ONS Estimated prevalence of COVID-19 in England. Click for a larger version.

Note these estimates come from random survey tests (so-called Pillar 4 tests), not clinical tests.

I have shown two curves on the graph above.

  • The black dotted line (– – –) is the same curve I have plotted for the previous thirteen weeks. (Link)
  • It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
  • The blue continuous curve is the ONS model for what is ‘really happening’.
    • I cannot explain how this estimate lies consistently below the data on which the model is based. Clearly there is something I have still not understood. I did ask ONS but they did not reply.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July.

Data for positive casesdaily hospital admissions and daily deaths. Click for a larger version. Recent details for each quantity are given in separate graphs at the head of the article.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days – the rate at which the epidemic declined during Lockdown#1.
  • The increasing trends correspond to quantities doubling every 15 days.

Back in July, the three data sets initially fell with similar time-dependencies and then rose through the autumn. The last week’s upswing is clear even on his logarithmic scale.

Data#3. Details and Projections

Because we are now in the non-exponential phase of the epidemic, I have re-plotted recent data for casesadmissions and deaths on a linear scale: these can be found at the top of the article.

I have also included some projections (as dotted lines) assuming that:

  • The effects of Lockdown#2 began to show through on Day 324,
  • The declines will be as swift as in Lockdown#1 (halving every 21 days).
  • The declines will continue after the 2nd December end of Lockdown#2.
  • The decline in hospital admissions is delayed 5 days with respect to cases
  • The delay in deaths is delayed 7 days (a change from last week) with respect to hospital admissions.

The curved dotted-line projections on the linear graphs at the graphs at the top of this article are effectively the same as the straight-line projections on the combined (logarithmic) graph. Please note that:

  • These are guidelines not predictions.
  • Look to see if quantities fall faster than this, or slower than this.

It is clear that the data are no longer following the hoped-for declining trends.

As I explained in a mid-week article (link) because cases lead to admissions which lead to deaths, we can use data for positive cases and  hospital admissions to predict deaths in the coming days and weeks. These projections are shown below.

Data for daily deaths. are shown as a solid black line. The yellow dotted curve (– – –) is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve (– – –) is the predicted daily death curve assuming 2% of cases die after 17 days. Click for a larger version.

The predictions based on hospital admissions are more reliable (I think) because they are less affected by the ‘fair- sampling’ issues when anticipating deaths from for cases.

These predictions suggest that in the coming week there might a further small fall in the death rate, but this will be followed by a increase later in the week or in the following week.

So…

In my opinion, it is all kicking off again:

  • And the government seem to have lost the will to act.
  • The lesson is very very clear: only the conditions of Lockdown have demonstrably reduced the rates of positive cases, admissions and deaths. Tier 3 measures may also achieve this but Tier 2 measures do not.
  • Failure to act immediately will mean that the death rate will be sustained at the level of roughly 400 people per day probably until late January. That would cause another 20,000 deaths by the end of January.
  • in my opinion Christmas should be officially cancelled with a planned delayed celebration and extended holiday at Easter time (4th April 2021).

Stay safe.

COVID-19: It’s simple: Cases >>> Admissions >>> Deaths

December 6, 2020

Data for daily deaths. are shown as a solid black line. The yellow dotted curve () is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve () is the predicted daily death curve assuming 2% of cases die after 17 days. Click for a larger version.

How epidemics work.

Friends: Allow me to explain how epidemics work. Cases lead to hospital admissions which lead to deaths.

  • People get ill – they become ‘a case’ identified by a positive COVID-19 test
    • A few days later (M days) a fraction of these people (x%) will die.
  • People are admitted to hospital
    • A few days later (N days) a fraction of these people (y%) die.

So what are M and N and x and y? For COVID-19, very approximately, M is 17, N is 7, x is 2 and y is 27: in other words:

  • People get ill – they become ‘a case’ identified by a positive COVID-19 test
    • Roughly 17 days later 2% (1 in 50) of these people will die.
  • People are admitted to hospital
    • Roughly 7 days later 27% (1 in 4) of these people will die.

How did I work out the numbers? 

I worked them out from the Government Coronavirus Dashboard statistics I have been plotting all year.

This is how the calculation is made. The logarithmic plot below shows cases, admissions and deaths since July. The curves are similar in shape.

Data for positive casesdaily hospital admissions and daily deaths. are shown as solid lines. The yellow dotted curve () is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve () is the predicted daily death curve assuming 2% of cases die after 17 days. A non-logarithmic version of this plot is shown below. Click for a larger version.

To find out the values of M and x, I multiplied the positive test data by x% and delayed it by M days. I then plotted it on the graph and above and adjusted M and x to get the best match with the actual data on daily deaths.

To find out the values of N and y, I multiplied the admissions data by y% and delayed it by N days. I then plotted it on the graph and above and adjusted N and y to get the best match with the actual data on daily deaths.

The match is not exact, but given the crudity of the model, the agreement across months is remarkable.

The major discrepancy is that in September, hospital mortality (deaths from admissions) was much lower than it is now: somewhere in the range 10% to 15%. Since hospitals are still generally coping, this is probably due to the age of people being admitted. Younger people have a much better survival rate.

Data for daily deaths. are shown as a solid black line. The yellow dotted curve () is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve () is the predicted daily death curve assuming 2% of cases die after 17 days. Click for a larger version.  A logarithmic version of this plot is shown above. Click for a larger version.

Comparison with the First Wave 

I carried out this kind of analysis during the First Wave of the pandemic (link, link, link).

Back then, COVID tests were only available in hospitals and so the data cannot be interpreted in the same way as now. But hospital admissions are still carried out on the same basis.

I was surprised to find that:

  • Hospital mortality has not obviously changed since April.

Still roughly a quarter of people admitted to hospital with COVID will die. There may be a few percentage points of change – but nothing very significant.

Why this matters 

Many people – it would be invidious to name them – want you believe the pandemic is over. It is not.

They see the appalling economic and social cost of the pandemic and want to prioritise economic and social well-being and temporarily ignore the virus. I sympathise with that desire.

But to advance their arguments they bring forward endless quibulations about some technical detail or another of COVID – false positives for example. Or claim that it is all a hoax.

But if the virus is ignored it will not be offended: it will just kill more people.

  • The lethality of the virus has not changed since the start.

I have written this just to show the simplicity of the viral progress: cases lead to hospital admissions which lead to deaths.

COVID-19: Day 338: Cases are falling, but the death rate is still very high.

December 5, 2020

Summary

Friends: Lockdown#2 is over and we have entered the vale of tiers.

The latest data are discussed below but the headline is this: the rates of positive tests and  hospital admissions are clearly declining but the rate of deaths is only showing the first hints of a decline.

Recent data for the number of daily positive tests and their 7-day retrospective average together with last week’s optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily hospital admissions and their 7-day retrospective average together with last week’s optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily deaths and their 7-day retrospective average together with an optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Also, as I noted last week, Lockdown#2 appears to have driven down cases at a similar rate to Lockdown#1. Let us hope that the new ‘Tiers’ can maintain that fall.

But…

  • with a 7-day-average death rate of 440 people per day we are still in a bad situation. In fact, it is amongst the worst in the world.
  • with viral prevalence only just below 1%, there is an ongoing risk that the death rate could again increase rapidly if adherence to restrictive measures lapses, such as while shopping, or at Christmas.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Data from Table 1d of the ONS: Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 28th November 2020 on average 0.86% of the UK population were actively infected, roughly 0.2% down on the previous week’s estimate.

The raw count of positive tests was:

  • 1,967 from 182,186 people tested in the two weeks to 28th November,
  • 2,096 from 163,054 people tested in the preceding two weeks, and
  • 1,931 from 163,434 people tested in the two weeks preceding that.

The data in the table above are graphed below.

ONS Estimated prevalence of COVID-19 in England. Click for a larger version.

Note these estimates come from random survey tests (so-called Pillar 4 tests), not clinical tests.

I have shown two curves on the graph above.

  • The black dotted line (– – –) is the same curve I have plotted for the previous eleven weeks. (Link)
  • It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
  • The blue continuous curve is the ONS model for what is ‘really happening’.
    • I cannot explain how this estimate lies consistently below the data on which the model is based. Clearly there is something I have still not understood. I did ask ONS but they did not reply.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July.

Data for positive casesdaily hospital admissions and daily deaths. Click for a larger version. Recent details for each quantity are given in separate graphs at the head of the article.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days – the rate at which the epidemic declined during Lockdown#1.
  • The increasing trends correspond to quantities doubling every 15 days.

Back in July, the three data sets initially fell with similar time-dependencies and then rose through the autumn.

Data#3. Details and Projections

Because we are now in the non-exponential phase of the epidemic, I have re-plotted recent data for cases, admissions and deaths on a linear scale: these can be found at the top of the article.

I have also included some projections (as dotted lines) assuming that:

  • The effects of Lockdown#2 began to show through on Day 324,
  • The declines will be as swift as in Lockdown#1 (halving every 21 days).
  • The declines will continue after the 2nd December end of Lockdown#2.
  • The decline in hospital admissions is delayed 5 days with respect to cases
  • The delay in deaths is delayed 7 days (a change from last week) with respect to hospital admissions.he hea

The curved dotted-line projections on the linear graphs at the graphs at the top of this article are effectively the same as the straight-line projections on the combined (logarithmic) graph. Please note that:

  • These are guidelines not predictions.
  • Look to see if quantities fall faster than this, or slower than this.

Out of curiosity I have also plotted the rate of hospital admissions and deaths relative to start of Lockdown for Lockdowns #1 and #2 below.

We see that the 7-day averages of hospital admissions rose for a clear two weeks after the start of Lockdown#1, and this has also happened in Lockdown#2.

Data for 7-day retrospective averages of daily hospital admissions relative to start of Lockdowns#1 and #2. Click for a larger version.

We also see that the 7-day averages of deaths rose for a 3 to 4 weeks after the start of Lockdown#1, and this has also happened in Lockdown#2.

Data for 7-day retrospective averages of daily deaths relative to start of Lockdowns#1 and #2. Click for a larger version.

So…

I am continuing to allow myself to feel encouraged: In the coming week I will be carefully watching the number of new cases to see if the falls achieved during Lockdown#2 can be maintained.

Stay safe.


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