Archive for the ‘Corona Virus’ Category

COVID-19: Day 142: Population Prevalence Projections

May 22, 2020
Actual (black) and Projected (red) UK daily deaths

How will the population prevalence of COVID-19 develop?

This is a question about the future and so – of course – the answer is “We don’t know“. But we can make some estimates based on our understanding of viral transmission.

I approached the question of the population prevalence of COVID-19 using a projection from Worldometer. Downloading the data, I mapped out how we might expect the rate of daily deaths to decline.

I feel bad that I don’t know the basis of the Worldometer model, but then I am only looking at the results semi-quantitatively. They will help to guide my expectations as the summer progresses.

The graph at the head of the article shows the 7-day rolling average of daily deaths as a black line, and the projection as a dotted red line. There are two features to notice:

  • The current death rate is still high: more than 300 deaths every day.
  • As we proceed into the summer the death rate reduces, falling below 100 a day in mid-June. The uncertainty in the projection is shown shaded between two finely-dotted lines.

However it is difficult to see both the large numbers and the small numbers on the same graph. So, time to use a logarithmic vertical axis! The graph below shows the same data as the previous graph, but plotted on a logarithmic axis.

Actual (black) and Projected (red) UK daily deaths plotted on a logarithmic vertical scale.

Now we can see the behaviour in the tail of the graph.

  • We expect the death rate to fall to 30 deaths per day, a factor 10 lower than at present, in 6 to 7 weeks – around 45 days. If events proceed closer to the lower projection, this could happen in as little as 35 days.
  • Projecting further it will fall to around 3 deaths per day, a factor 100 lower than at present, in around 90 days – this is around the start of September and the new school term. If events proceed closer to the lower projection, this could happen in as little as 70 days.

However, the rate at which people die does not tell us about the hazard that we personally face.

A better indicator of personal hazard is the prevalence of ill people in the population.

Population Prevalence Projection

As shown on both figures in blue, a survey between 4th and 17th of May found a population prevalence of ill people of 1 in 400 – or 2500 people in every million people were ill with COVID-19.

Assuming that the population prevalence changes at the same rate as deaths, the graph below shows how the ill population might be expected to decline with time.

Estimated population prevalence of people actively ill with COVID-19

The coarsely dotted red line is based on the central projection from the first two graphs. The lower dotted red line is based on the more optimistic projection in the graphs above. Based on these slightly optimistic projections we expect:

  • Around the start of June, the population prevalence should be just less than 1000 per million.
  • Sometime in August we can expect the population prevalence to have fallen by a further factor 100 to around 10 per million.
  • At the start of the school term in September, the population prevalence might possibly be as low as 1 in a million.

These very low levels of population prevalence still hold the possibility for viral growth and so social distancing measures would still be required.

Additionally, as international travel resumes, new sources of viral transmission will fly into the country

But at these very low levels, the severity of restrictions on schools and large gatherings could be much more relaxed, especially if a strong contact tracing service was available at that time.

In the next article I will look at where the virus will go “In the end”!

COVID-19: Day 139: Are we ready to re-open schools?

May 19, 2020


Where are we now? 

We are now in the end-part of the first phase of the Corona virus 2020 tour of the UK.

The graph of ‘deaths in all settings’ is shown above. Today (day 139) the trend rate of deaths is roughly 350 deaths-per-day, and it is falling at about 125 deaths-per-day every week.

If the linear trend continued the death rate would fall close to zero deaths-per-day in mid-June. It is more likely that the rate of decline of the death rate will flatten off into a long tail as shown in the UK projection from Worldometer below.


Additionally, random testing amongst the UK population during the period 1 May to 10 May (day 121 to day 130). During this period researchers concluded that roughly 1 in 400 individuals were actively ill with COVID-19). This specifically excluded people with direct links to care homes or hospitals.

Full Re-opening of Schools

By 1st June the prevalence of sick individuals amongst the population is likely to have fallen further – it will probably be in the region of 1-in-1000 across the country.

At the 1-in-1000 level, with appropriate precautions, a large number of activities become very low risk. Why? Because the chance of meeting an infected individual is low, and social distancing means that even if an individual is infected, the chance that they will infect you is low.

But not all activities are low risk. And schools, where groups of roughly 1000 individuals gather joyously together, are one such place.

Schools contain people who are likely to practice social distancing only imperfectly. They also contain large numbers of shared touchable surfaces (hand rails, door knobs, gym equipment, laboratory kit, taps etc).

If schools re-opened fully on 1st June (Day 152 of 2020), then it would be more likely than not that every large school would contain an infected individual.

Personally, I would not consider this acceptable. Fully re-opening with a prevalence of infected individuals around the 1-in-1000 level would virtually guarantee that every school would seed new outbreaks that could then affect vulnerable people. When these inevitably occurred, the school would need to be shut in any case.

By September (another 92 days on from June 1st), with good fortune and continued efforts, the projection above indicates that the population incidence of corona virus might conceivably be more than 100 times lower (10 in a million). At this rate only 1 in 100 schools would be likely to contain an infected individual.

At this level, I think it would be possible to safely re-open schools with minimal risk and minimal precautions. One would probably seek to segment the population into smaller groups to enable contact tracing and isolation when the inevitable cases did occur.

Government Plans for 1st June

The government plan a partial school re-opening on 1st June. This will involve only between one quarter and one third of school places being filled. This reduces the chance that a school will contain an infected individual such that we could reasonably expect one infected individual in only every three or four schools.

Is that rate low enough? Personally I think not. And a Minister speaking in a pompous and condescending tone and implying that teachers do not have children’s interests at heart would not convince me. I doubt it convinces many teachers.

The judgment involves a balance of risks and benefits. As I see it:

  • The move would bring no benefit to the 67% to 75% of students who were not attending school.
  • For the 25% to 33% of the pupils who would attend, I would think there would  need to be some overwhelming and obvious benefit of the proposal in order to justify the extraordinary amount of trouble required to reconfigure schools. I don’t know what that benefit is nor how it could be delivered in 7 weeks.
  • At a population incidence of 1-in-1000, many schools would definitely harbour infected individuals, but the infrastructure for tracking and tracing people is not yet in place.

Personally, I think re-starting schools on 1st June has no overwhelming benefit. But at a population incidence of COVID-19 of 1-in-1000, it has many risks.

In September – if we all wash our hands and keep our distance – the population prevalence of corona virus should be low enough that near-normal operation of schools should be possible. And teachers and pupils can then focus mainly on teaching and learning. Wouldn’t that be nice :-).


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)


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.




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


  • 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.


  • 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.


  • 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.


  • 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.

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.

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


  • 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.


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.


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.



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.


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 121: Reasons to be cheerful. One, Two, Three.

May 1, 2020

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

Today – May 1st – is Day 121 of 2020 and I greet this day with a lightness of spirit I have not experienced for many years.

Why do I feel so good? Because yesterday I left NPL! That’s the first reason to be cheerful!

I’ll write more about my disaffection with NPL in due course, but for now let’s take another look at the data on the pandemic. And there we find two more reasons to be cheerful!

Back to the Pandemic

On Day 111 of 2020, the rate at which people were being admitted to hospital with COVID-19 (Pillar 1 test results) was declining, but slowly. A linear fit to the trend indicated that zero admissions would not be reached until roughly day 165 of 2020: 14th June:


Re-plotting the same data today, Day 121 of 2020, the same linear fit suggests that zero admissions will be reached around day 145 of 2020: 25th May 2020 – three weeks earlier!

So the decline in the rate of cases is steeper than it initially appeared – that is a second reason to be cheerful!


So when should we end the ‘Lock Down’?

Looking at the graph above it might seem that extending the lock-down out to day 145 would be appropriate. But in fact, it could make good sense to begin opening up well in advance of that. Why?

Yesterday (Day 120), 3059 people were Pillar-1 tested with COVID-19 as they entered hospital. These people were infected typically 18 days previously i.e. around day 102.

If the rate of Pillar-1 tested admissions is declining at 700 cases per week now, then this must be because roughly 18 days previously, new infections were declining at the same rate. So we can plot the implied rate of infection.


The implication of this analysis is that the rate of new infections across the entire UK is currently close to zero.

If, out of a sense of precaution, we allowed (say) 10 days more, then it seems to me that there would be very little risk in opening things up after, perhaps, day 137 – May 11th.


I have not included any analysis of care homes and similar care settings in this or any of my earlier blogs. But it seems that a disaster is still unfolding there.

Aside from the disaster of events in care homes in themselves, the presence of ‘hot’ infection sites leaves open the possibility of seeding further cases among residents, carers, and all who come into contact with them.


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.


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.


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


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.


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.

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?


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.


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.


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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