Archive for the ‘Personal’ Category

R<1 is not enough: we need R<<1.

May 29, 2020

I am getting heartily fed up with the government’s daily ‘Number Theatre’ as David Spiegelhalter calls it. So many numbers, but so little meaningful insight into what is happening.

We are all repeatedly informed that we need the reproduction number to be less than unity (i.e. R< 1) in order to drive down the prevalence of the disease. But it is generally not stressed how extraordinarily hard this is, and how we really need R to be very much less than unity i.e. R<<1

Individuals are integers

R is expressed as a decimal fraction, but for any individual ill person, the number of people they infect is an integer not a fraction i.e. it could be:

  • 0 – ideally.
  • 1 – almost inevitably
  • 2 or more – quite easily

So to achieve R = 0.9 for ten ill people, the number of people infected could be:

  • 1,1,1,1,1,1,1,1,1,0 i.e. 9 people infect one other person, but one hero manages to infect no-one else.
  • 2,1,1,1,1,1,1,1,0,0 i.e. 1 person infects 2 other people – it’s easily done. Now to achieve R = 0.9 we need two zero-infection heroes.
  • 3,1,1,1,1,1,1,0,0,0 i.e. 1 person infects 3 other people – it’s easily done. Now to achieve R = 0.9 we need three zero-infection heroes.

In all of these cases – there are still many infectious people after a single ‘generation’ of transmission.

For a disease which can be infectious before people know they are ill, it is extraordinarily hard not to infect at least one other person. It has taken the disruption of our “lockdown” to achieve R in the range 0.7 to 0.9.

The situation above describes only transmission across one ‘generation’ of the virus. What happens when we trace infections down a chain? When we do this we find that chance fluctuations really matter.

Fluctuations really matter

To see the effect of fluctuations I created a simplified spread sheet model to track infections across 4 generations.

  • I started with a single infected person and tried to calculate the number of people who would be infected after 4 generations of transmission.
  • I simplistically assumed each infected person had a chance of infecting two other people, each with a probability R/2 to make a total transmission probability of R.
  • I then used Excel’s random number generator to produce a random number between 0 and 1.
  • If the random number generator produced a number less than R/2, then infection took place, otherwise no infection took place.

I then repeated this for three more generations and at the end I asked – how many people are infected now? I repeated the experiment 50 times for different values of R and the results are shown below.

On average, the numbers of people infected after 4 generations (red dots) were close to what would be expected i.e. R4, shown as a grey line. But the fluctuations were very significant. On the graph above I have shown in green the maximum number of people infected in at least 1 of the 50 simulations

  • During 50 experiments at R = 0.9, I twice observed that there were 4 infected patients after 4 generations of transmission when we would have expected (on average) only 0.65 of an infection.
  • During 50 experiments at R = 1.0, I observed on one occasion that there were 7 infected patients after 4 generations of transmission when we would have expected (on average) only a single infection .

This shows that even when the average R value is below unity, and infection clusters might be expected to die away on average. Fluctuations mean that it is possible – indeed likely – that some single infections can persist for many generations of transmission and in fact grow into clusters and seed a new outbreak.

Where we are now?

As Louis Armstrong might have said, I don’t get around much anymore. But on my expeditions out, I see many more people than at the height of the “lockdown”. It is also not hard to see some groups of people who do not appear to be social distancing.

If the “lockdown” achieved R = 0.7, then I would estimate that the R value now must be higher, probably close to 1. The point of this article is to say that that even for R values below 1 on average, fluctuations can allow a single infection to grow into a significant cluster over several generations.

The ONS estimates that there are roughly 133,000 people currently infected with the virus. Even with R=0.9 it will take until the end of the year to reduce the number of infections to 10,000 – still a massive number. Over that length of time, and as economic and social activities resume, there will be thousands of opportunities for small outbreaks to grow significantly.

In my opinion, with this infection rate and a likely transmission rate R close to unity, there is a strong likelihood of significant further outbreaks. 93% of our population is still susceptible and if the death rate were similar to what we have seen already we could potentially lose 10 times more people than we have already.

I understand the economic and social imperatives that are driving us towards re-opening the economy. But personally I am skeptical that the virus is sufficiently under control to allow re-opening without many further outbreaks. I do hope I am wrong.

This is what clarity looks like

May 11, 2020

At this difficult time, I thought I might offer my assistance to the UK government by showing them what clarity looks like. It looks like this (pdf here)

Slide2

This is New Zealand’s summary of how they intend to respond to each level of threat.

The measures seem reasonable, but I am not advocating for or against them. My point is that in New Zealand everyone knows what they are!

They can look ahead and see what will and won’t be allowed in the future

One of the important advantages of clarity is that if there is a mistake in the guidance – too weak or too strong – it can be changed.

In contrast the UK’s instructions are clearly the product of confused and conflicted discussions – and so individuals are left unsure precisely what they are expected to do.

Here is the kiwi guidance in more detail.

Threat…

Slide3

…Response

  • These responses are cumulative i.e. All level 3 restriction apply at level 4.
  • The responses can be either local or national

LEVEL 4

  • People instructed to stay at home in their bubble other than for essential personal movement.
  • Safe recreational activity is allowed in local area.
  • Travel is severely limited.
  •  All gatherings cancelled and all public venues closed.
    Businesses closed except for essential services (e.g. supermarkets, pharmacies, clinics, petrol stations) and lifeline utilities.
  • Educational facilities closed.
  • Rationing of supplies and requisitioning of facilities possible.
  • Reprioritisation of healthcare services.

LEVEL 3

  • People instructed to stay home in their bubble other than for essential personal movement – including to go to work, school if they have to, or for local recreation.
  • Physical distancing of two metres outside home (including on public transport), or one metre in controlled environments like schools and workplaces.
  • People must stay within their immediate household bubble, but can expand this to reconnect with close family / whānau, or bring in caregivers, or support isolated people. This extended bubble should remain exclusive.
  •  Schools (years 1 to 10) and Early Childhood Education centres can safely open, but will have limited capacity. Children should learn at home if possible.
  • People must work from home unless that is not possible.
  •  Businesses can open premises, but cannot physically interact with customers.
    Low risk local recreation activities are allowed.
  •  Public venues are closed (e.g. libraries, museums, cinemas, food courts, gyms, pools, playgrounds, markets).
  • Gatherings of up to 10 people are allowed but only for wedding services, funerals and tangihanga. Physical distancing and public health measures must be maintained.
  • Healthcare services use virtual, non-contact consultations where possible.
  • Inter-regional travel is highly limited (e.g. for essential workers, with limited exemptions for others).
  • People at high risk of severe illness (older people and those with existing medical conditions) are encouraged to stay at home where possible, and  take additional precautions when leaving home. They may choose to work.

LEVEL 2

  • People can reconnect with friends and family, go shopping, or travel domestically, but should follow public health guidance.
  • Physical distancing of two metres from people you don’t know when out  in public is recommended, with one metre physical distancing in controlled environments like workplaces, unless other measures are in place.
  • A phased approach to gatherings – initially no more than 10 people at any gathering. This applies to funerals, tangihanga, weddings, religious ceremonies and gatherings in private homes. Restrictions reviewed regularly.
  • Sport and recreation activities are allowed, subject to conditions on gatherings and contact tracing requirements, and – where practical – physical distancing.
  • Public venues (museums, libraries, etc.) can open but must comply with public health measures. Gatherings rules do not apply to public venues as long as people are not intermingling.
  • Health and disability care services operate as normally as possible.
  • Most businesses can open to the public, but must follow public health guidance including in relation to physical distancing and contact tracing. Alternative ways of working encouraged where possible (e.g. remote  working, shift-based working, physical distancing, staggering meal breaks, flexible leave).
  • It is safe to send your children to schools, early learning services and  tertiary education. There will be appropriate measures in place.
  • People at higher-risk of severe illness from COVID-19 (e.g. those with underlying medical conditions, especially if not well-controlled, and seniors) are encouraged to take additional precautions when leaving home.
  • They may work, if they agree with their employer that they can do so safely.

LEVEL 1

  • Border entry measures to minimise risk of importing COVID-19 cases.
  • Intensive testing for COVID-19.
  • Rapid contact tracing of any positive case.
  • Self-isolation and quarantine required.
  • Schools and workplaces open, and must operate safely.
  • Physical distancing encouraged. No restrictions on gatherings.
  • Stay home if you’re sick, report flu-like symptoms.
  • Wash and dry hands, cough into elbow, don’t touch your face.
  • No restrictions on domestic transport – avoid public transport  or travel if sick.

Farewell to my NPL colleagues

May 9, 2020

It’s been just a week now since I stopped working at NPL, and my sense of relief has not abated.

I was sad not able to say goodbye in person to many kind friends and colleagues. But I would like to thank the 60 or so friends who took the time to attend a ‘Zoom’ party (below) with me.

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It was not as weird as I feared! I had the chance (I think) to at least say “Hello and Goodbye” to everyone. And on the plus side I did not get as drunk as I might have done had we gone to a pub.

Anyway, it was lovely to see you all. And I wish you all the best for your futures – at NPL or beyond.

 

 

COVID-19: Day 127: I feel less optimistic

May 7, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.
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In my last post (on day 121 of 2020) I indulged in a moment of optimism. I am already regretting it.

What caused my optimism?

My optimism arose because I had been focusing on data from hospitals: the so-called ‘Pillar 1’ data on cases diagnosed as people entered hospital, and the subsequent deaths of those people in hospital.

These were the data sets available at the outset, and they tell a story of a problem in the process of being solved.

My last post pointed out that each new ‘Pillar 1 case’ arose from an infection roughly 18 days previously. Applying a trend analysis to that data indicated that the actual rate of ongoing infection that gave rise to the Pillar 1 cases must currently be close to zero.

I think this conclusion is still correct. But elsewhere – particularly in care homes and peripheral settings – things are not looking so good.

Pillar 1 versus Pillar 2 Testing

Although each Pillar 1 or Pillar 2 ‘confirmed case’ designates a single individual with the corona-virus in their body, the two counts are not directly comparable.

  • Cases diagnosed by Pillar 1 testing correspond to individuals who have suffered in the community but their symptoms have become so bad, they have been admitted to hospital.
  • Cases diagnosed by Pillar 2 testing correspond to a diverse range of people who have become concerned enough about their health to ask for a test. This refers mainly to people working in ‘care’ settings.

Diagnosing Pillar 2 cases is important because they help to prevent the spread of the disease.

But whereas a Pillar 1 case is generally very ill – with roughly a 19% chance of dying within a few days – Pillar 2 cases are generally not so ill and are much less likely to lead to an imminent death

Summarising:

  • Around 19% of Pillar 1 ‘Cases’ will die from COVID-19.
  • In Pillar 2 ‘Cases’ the link is not so strong, but these cases give an indication of the general prevalence of the virus.

We should also note that as the number of tests increases, the indication of prevalence given by Pillar 2 diagnoses will slowly become more realistic.

What does the data say: 3 Graphs

Graph#1 shows the number of cases diagnosed by Pillar 1 and Pillar 2 testing.

Slide1

Pillar 1 diagnosed cases are falling relatively consistently: this is what led to my aberrant optimism. However Pillar 2 cases are rising.

This rise in part reflects the higher number of tests. But it more closely reveals the true breadth of the virus’s spread. This rise is – to me – alarming.

Graph#2 below shows Pillar 1 and Pillar 2 cases lumped together. This shows no significant decline.

Slide2

However, because deaths are more closely associated with Pillar 1 diagnoses, the number of daily deaths (Graph#3) is declining in a way more closely linked to the fall in Pillar 1 cases.

Slide3

Overall 

The NHS is coping – but the situation outside of hospitals looks like it is still not under control.

This reality is probably a consequence of the long-standing denial of the true importance of the care of elderly people, and the attempt to ‘relegate’ it from the ‘premier league’ of NHS care.

Considering the forthcoming lightening of regulations, it seems likely that viral spread in the community as a whole is currently very low. Thus a wide range of activities seem to me to be likely to be very safe.

But the interface between high risk groups – care workers in particular – and the rest of us, is likely to be area where the virus may spread into the general population.

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Discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19: Day 115: About half-way through.

April 25, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Today is Day 115 of 2020 and as I stare again at the COVID-19 data, two things seem particularly striking.

The first thing is that – as we pass 20,000 deaths – we are only halfway there. My expectation is that another 20,000 people will yet die from from COVID-19 over the next 50 days or so.

And the second thing is that on Monday March 23rd, when the UK ‘locked down’ – the cumulative number of deaths was 280. This is less than 1% of the number of people who would eventually die. And yet at that point, we were in some sense already committed to the astonishing total of deaths we are facing.

Thing#1: Halfway 

I have been look ahead to see what we might expect to happen in the coming days and weeks.

I assumed that:

  • 19% of people diagnosed with COVID-19 using ‘Pillar-1’ testing in hospitals will die after – on average – 6 days. This is 1% less than I assumed previously, but seems to match the recent data better.
  • The number of Pillar-1 confirmed cases is declining linearly. These are mainly patients being admitted to hospital.

Based on these assumptions I have calculated the expected cumulative totals of confirmed cases and consequent deaths.

Slide1

The above graph shows various statistics plotted versus the day of the year.

  • The vertical green lines show the date of the ‘lock down’, the end of ‘phase 1’ of the ‘lock down’, and the upcoming end of ‘phase 2’.
  • The blue curve shows the cumulative number of ‘Pillar 1 tested’ COVID-19 cases.
  • The red curve shows the cumulative total of COVID-19 deaths in hospital.
  • The black dotted line shows the predicted number of deaths based on
    • 19% case mortality after 6 days.
    • A continuation of the current linear decline in Pillar 1 cases.

There is considerable uncertainty in this projection. But I think it represents a fair expectation.

It indicates that in terms of deaths,
we are still only half-way through.

Thing#2: Growth Rate

Slide2

The above graph shows various statistics plotted versus the day of the year.

  • The vertical green lines show the date of the ‘lock down’, the end of ‘phase 1’ of the ‘lock down’, and the upcoming end of ‘phase 2’.
  • The blue curve shows the cumulative number of ‘Pillar 1 tested’ COVID-19 cases.
  • The black dotted line shows the predicted number of cases based on a continuation of the current linear decline in Pillar 1 cases.

There is considerable uncertainty in this projection. But I think it represents a fair expectation.

What also struck me here was that on Day 81, at the start of the original ‘lock down’, there had only been 280 deaths and the daily death rate was about 50 people per day. And yet this relatively small number was a sign of a tsunami of illness about to overwhelm our country.

By acting then we have undoubtedly saved the lives of probably hundreds of thousands of people.

Thing#3: Life after Day 123 (3rd May)

On day 123, the cumulative total of people testing positive for the corona virus as they entered hospital will be approximately 150,000. 

Based on the loose statistic that 20% of people require hospital treatment, we can guess that

  • the cumulative number of true cases in the population is around 750,000.
  • a significant fraction of these people will have had the illness and recovered.

Thus after 3rd May, the number of people who will be unwell will be much less than 1% of the population.

So relying on chance alone, for every 100 people one meets, 99 will be virus free.

It seems to me that even with substantial relaxation of our current social distancing, it will likely be possible to keep the chance of person-to-person virus transmission low.

But given the sensitivity I mentioned in Thing#2 – we will need to remain vigilant.

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Discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19: Day 111:Getting better, but too slowly.

April 21, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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This post looks at today’s data (Day 111) and clarifies the meaning of the data classification “New Cases”.

This change gives a small downward trend to the predicted number of daily deaths. The slowness of this trend – if continued – would result in our national ordeal lasting through to mid-June, with a final death toll in excess of 40,000.

‘New Cases’

In my previous posts (12, 3), I have been predicting the number of hospital deaths one week ahead of time by reasoning that mortality from COVID-19 hospital admissions is around 20% and so 20% of new ‘Cases’ become ‘Deaths’ after 6 days on average.

One important qualification to this prediction is that ‘New Cases’ are evaluated in the same way across the period. In fact the way the statistic for ‘New Cases’ is derived was changed on April 11th (Day 101 of 2020).

Pillar 1 & Pillar 2 Testing

I had been alert to this possibility, but I only became aware of this change yesterday during the government briefing, when they showed this slide.

Slide2

I searched for the data on line but could not find it.

[Update: I found the slides from the daily government briefings here.]

So I captured this by freezing a replay of the presentation and then pressing ‘Print screen’ on my computer. I then typed the number of cases from the blue and orange categories into my spreadsheet.

  • Initially, ‘New Cases’ cases were all deduced by so-called Pillar 1 testing (blue). This is mainly the hospital tests of new admissions.
  • From March the 29th, a small number of cases deduced from Pillar 2 testing (orange) of health care staff were being taken, but these were not included with the Pillar 1 data.
  • From April 11th, the increasing number of cases deduced from Pillar 2 testing (orange) of health care staff were included with the Pillar 1 data.

The effect of this made it seem as if the number of cases from Pillar 1 testing – the statistic we would expect to correlate with later deaths – was staying high when in fact it is slightly declining.

In itself, this is good news. But it is not very good news, because the reduction in cases diagnosed by Pillar 1 testing is not very great.

Revised Predictions

Below I have re-plotted my usual graph but now the prediction for future deaths is based just on Pillar 1 testing

Slide3

The above graph shows various statistics plotted versus the day of the year.

  • the blue curve shows the daily published number of new ‘Pillar 1 tested’ COVID-19 cases.
  • the red curve shows the daily number of COVID-19 deaths in hospital.
  • the black dotted line shows the predicted number of deaths based on 20% case mortality after 6 days.
  • The blue dotted line shows my previous prediction based on ‘New Cases’ diagnosed by Pillar 1 and Pillar 2 testing.
  • The vertical green lines shows the start and end of the first phase of the ‘lock down’

For the part of the curve relating to the last two weeks, the data are not changing rapidly, so we can re-plot the data on a linear vertical scale to see that region in more detail.

Slide4

The above graph shows some of the same data as the previous graph.

  • the red curve shows the daily number of COVID-19 deaths in hospital.
  • the black dotted line shows the predicted number of deaths based on 20% case mortality of Pillar 1 cases after 6 days.
  • the blue dotted line shows my previous prediction based on ‘New Cases’ diagnosed by Pillar 1 and Pillar 2 testing.

What I conclude from this data is that:

  • The number of new cases diagnosed by Pillar 1 testing is falling, but only slowly.
  • Fitting a linear trend to the data (see the graph below) the number of new cases would not be expected to reach zero for another 54 days  – Day 165 (14th June).
  • I do not know why this statistic is falling so slowly, and that worries me.
  • If that trend were followed, the death toll would likely exceed 40,000 – a truly appalling outcome.

Slide5

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Discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19: Day 107: I am concerned

April 17, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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In the last couple of posts (1, 2), I have explained that it is possible to predict the number of people who will die from COVID-19 in a week’s time by looking at the number of cases confirmed today.

Day 107 of 2020

Slide1

The above graph shows various statistics plotted versus the day of the year.

  • the blue curve shows the daily published number of COVID-19 cases.
  • the red curve shows the daily number of COVID-19 deaths in hospital.
  • the black dotted line shows the predicted number of deaths based on 20% case mortality after 6 days.

With more data, I have revised my estimate of mortality (deaths ÷ cases) down from 25% to 20%, but the estimated time-to-death has shortened from 7 days to 6 days.

As the graph above shows, there has been no fall in the number of cases diagnosed and so the last 4 weeks of data lead us to expect that there will be no fall in the death rate – over 800 people each day – for at least another week.

Concerning

This is very concerning and indicates that whatever we are doing now is failing to eliminate the virus from circulation.

If I were in charge – I would want to know why the number of cases is not falling. If I didn’t know, I would recommend even more stringent lock down measures.

Why? Because by day 130, (4th May) I think our collective tolerance and forbearance will become severely strained. If the end is not in sight, and if that curve remains flat, then as the combined costs  (economic, social, personal, and medical) grow, I fear there may be social unrest and an already appalling situation will become uncontrollable.

The final toll

Slide2

The above graph shows various statistics plotted versus the day of the year.

  • the blue curve shows the running total of COVID-19 cases.
  • the red curve shows the running total COVID-19 deaths in hospital.
  • the black dotted line shows the predicted number of deaths based on 20% case mortality after 6 days.

At day 107, there have been 14,576 confirmed UK COVID-19 deaths. If today’s cases become death statistics in 6 days as they have for the last 4 weeks, then the total number of deaths will exceed 20,000 before the daily death rate has even begun to fall.

Earlier on in the crisis, it looked like the death toll could be kept well under 20,000. But that now looks impossible.

Until the number of daily cases begins to fall, it will be impossible to estimate how long our current ‘lockdown’ will need to last, and how great a cost we will all have to pay.

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As I mentioned, discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19 Hospital Mortality

April 12, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Yesterday, I concluded that the mortality of UK COVID-19  patients entering hospital i.e. people already seriously ill with COVID-19, was roughly 25%. I was shocked at this large figure.

Sadly, after further investigation it appears to be increasingly plausible.

UK hospital deaths versus age

UK Government data is available in a spreadsheet downloadable from a link on the COVID-19 ‘Dashboard’

The data show the age ranges of people who have died from COVID-19 in hospital. The age ranges are rather broad but I have taken the liberty of drawing a smooth line through the data points.Slide4Based on this data (and also shown on the graph) is my calculation of the average age of people dying in UK hospitals from COVID-19: it is approximately 74 years of age.

However this data does not tell us how many people in these age ranges were admitted to hospital, so we cannot calculate the mortality.

 

US hospital mortality versus age

The Washington Post has an article which includes data on COVID-19 mortality in US hospitals admissions versus age. The data is based on the admission of 6479 patients since 1st March 2020.  I have re-plotted the data below.

Slide5

This mortality is for US hospitals, rather than UK hospitals, but assuming that treatment is similar, then we can look at the expected mortality for patients at the average age of death of UK patients. This is shown below below with a red horizontal line indicating 25% mortality.

Slide6

This data seems self-consistent.

  • The relationship between UK daily cases and UK daily deaths that I discussed yesterday seems to indicate that mortality is around 25%.
  •  US mortality data shows that at the average of UK deaths, mortality for hospital admissions is 25%.

Ideally we would also like to know the ages of UK patients at admission, but I could not find that data.

Discussion

Notice that this only concerns patients who are admitted to hospital i.e. patients who are already poorly and who have generally been suffering at home. Most people recover at home without needing medical care.

But even so, I have again been saddened by this result which makes it less likely that yesterday’s analysis was in error.

This support gives increased confidence to the prediction  that the number of daily deaths for the next 7 days is unlikely to fall significantly, because these deaths correspond to people who have already been admitted to hospital.

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As I mentioned, discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19 Numerology

April 11, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Life is very pleasant for me and my wife in this ‘stay at home’ world, but I find myself permanently anxious and neurotically focused on ‘the numbers’: trying to understand them and use them to foresee what’s coming next.

I had thought naively that the ‘lock down’, which started on Day 81 of the year, would be completely effective, and that new cases of COVID-19 would begin to decline. But as the data below shows, that doesn’t seem to have happened.

Slide1

The number of new cases has stopped rising – but new cases are still occurring at around 4500 ± 500 cases per day.

As I understand the data, and the way in which testing is done, these are mainly people entering hospital. People who have probably been ill at home for some time, but their symptoms have now become serious enough for them to come to hospital.

But even so, some of those people will have been infected after Day 81.

Relating New Cases to Deaths

Some fraction of the people entering hospital will die a few days later.

I have looked at the UK data to try to understand how many people would die – the fractional mortality – and the delay.

To do this I took the ‘new cases‘ data and:

  • Applied a delay to the data that moves it to the right on the graph
  • Adjusted the fractional mortality to try to match the statistic for daily deaths. This moves it downwards on the graph.

Slide2

I found a reasonable match to the data for a delay of 7 days and a fractional mortality of 25%. i.e. the data seem to imply that 1 in 4 people being admitted to hospital as a new case will die, on average just 7 days later.

Slide3

Is this right?

Well obviously I don’t know if this is right or not.

I had expected a much lower mortality for people entering hospital – perhaps 1 in 10. On the graph above this would push the dotted black curve downwards.

But if that were so, then in order to match the ‘daily deaths’ data, the time to death would have to be very short, and in fact the curve doesn’t match the data well.

I found that reasonable matches could be obtained with:

  • mortality of 30%  and a time until death of around 9 days,
  • mortality of 20%  and a time until death of around 5 days,

But the best match (by eye) seemed to be with a mortality of 25%  and a time until death of around 7 days,

Discussion

I was shocked and saddened by this result. I hope I have missed something out or misinterpreted the data. Perhaps the mortality or time until death have improved throughout the last few weeks.

A mortality rate of 25% has been reported in the ‘worst hit’ hospitals, but I assumed this was exceptional. Also, the time until death seemed much faster than I had expected.

One additional feature of this analysis is that – if correct – it predicts the number of daily deaths for the next 7 days. And the prediction is disappointing.

The analysis indicates that the number of daily deaths in the next 7 days is unlikely to fall because these deaths correspond to people who have already been admitted to hospital.

Link to Excel Spreadsheet: Modelling Death Delay and Mortality

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As I mentioned, discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try understand what is happening.

 

Life beyond lock-down: Masks for all?

April 3, 2020

Michael in a mask

Will we all be wearing masks in public for the next year or two?

A good friend sent me a link to a video which advocated the wearing of masks in public as a successful strategy for combating the transmission of corona virus.

I have no idea if this is true or not.

One thing of which I have been reminded by the current pandemic is that my intuition gained by experience as ‘an expert’ in one area, is not transferable. This pandemic has left me in a permanent state of bewilderment.

One of the key pieces of evidence offered in the video is the effectiveness of even primitive masks in inhibiting virus transmission in Czechia. Apparently,  mask-wearing in public has become de rigeur in Czechia, and there is – apparently – a low incidence of COVID-19 in Czechia.

I decided to look at the data

The table at the end of this article is compiled by data from Wikipedia’s list of the countries of Europe and their population, and the number of deaths recorded on Worldometer on the evening of 2nd April 2020.

The map below shows the results with the numbers expressing the numbers of deaths per million of the population.

[Note: Many European countries have small populations – less than the size of London – and many may not have good reporting of the deaths, which are in any case small in number. But the data is what it is.]

Number of deaths per million of population of countries in Europe on 2nd April 2020. See text for details. Data Table at the end of the article.

Number of deaths per million of population of countries in Europe on 2nd April 2020. See text for details. Data Table at the end of the article. Czechia is highlighted in yellow.

Does this data provide evidence that Czechia is a special case?

No.

To me it looks like Eastern Europe is generally less affected than Western Europe, and Czechia is in the middle. On the West it is bordered Germany and Austria, both of which have a low incidence (for Western Europe) per million of their population.

The 4 deaths per million of its population of its 10.7 million does not stand out as being anomalously low compared with, say, Poland (2 deaths per million of its population of 38 million) or Greece (5 deaths per million of its population of 10.4 million).

One further piece of evidence to look for would be the rate of growth of the virus within Czechia.

NYT Tracker for Czechia

The New York Times death tracker shows that the doubling-time for deaths in Czechia is similar to other countries in Western Europe – around 3 days.

The number of deaths are small and so the trend is uncertain, but it does not look like it is in the same group as Japan or South Korea which have only slow growth of virus-related deaths – a doubling time of more than 7 days.

In short, even though the idea of wearing a mask in public is not unreasonable, the data themselves do not seem to speak to the effectiveness of the habit.

But..

After the lock-down has ended, we all will need to be able to get out and about again and earn the money to pay for this hiatus. But the virus will still be out there and will still be exactly as lethal as it has been for these last few months.

So it might easily be that wearing a mask in public – proven in effectiveness or not –  may become a sign of respect for one’s fellow citizens.

One of the attractive features of the policy in Czechia is that the masks are not considered as being defensive i.e. protecting the wearer. Instead they are considered as a sign of pro-social behaviour i.e. a sign of one’s consideration of others.

Masks are unlikely to do any harm, and they may even do some good. But whichever is the case, it seems that in the US – the leader for many trends for both good and ill – their adoption may become mandatory.

NYT Tracker for Czechia

Headlines from papers on 2nd April 2020

So perhaps we will all be wearing masks in public for the for next year or two. I certainly didn’t see that coming!

UPDATE on 04/04/2020 ARTICLE ON ARS TECHNICA referencing new US CDC recommendations.

Data

Country Population Deaths @2/4/2020 Deaths/million
Germany 83,783,942 1,107 13
United Kingdom 67,886,011 2,921 43
France 65,273,511 5,387 83
Italy 60,461,826 13,915 230
Spain 46,754,778 10,348 221
Ukraine 43,733,762 22 1
Poland 37,846,611 57 2
Romania 19,237,691 115 6
Netherlands 17,134,872 1,339 78
Belgium 11,589,623 1,011 87
Czech Republic (Czechia) 10,708,981 44 4
Greece 10,423,054 53 5
Portugal 10,196,709 209 20
Sweden 10,099,265 308 30
Hungary 9,660,351 21 2
Belarus 9,449,323 4 0
Austria 9,006,398 158 18
Serbia 8,737,371 31 4
Switzerland 8,654,622 536 62
Bulgaria 6,948,445 10 1
Denmark 5,792,202 123 21
Finland 5,540,720 19 3
Slovakia 5,459,642 1 0
Norway 5,421,241 50 9
Ireland 4,937,786 98 20
Croatia 4,105,267 7 2
Moldova 4,033,963 6 1
Bosnia and Herzegovina 3,280,819 16 5
Albania 2,877,797 16 6
Lithuania 2,722,289 9 3
North Macedonia 2,083,374 11 5
Slovenia 2,078,938 17 8
Latvia 1,886,198 0 0
Estonia 1,326,535 11 8
Montenegro 628,066 2 3
Luxembourg 625,978 30 48

 


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