Posts Tagged ‘COVID-19’

COVID-19: Day 157: Population Prevalence Projections

June 6, 2020

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

Previously (link), I made estimates of likely prevalance of COVID-19 in the UK population by combining:

  • A projection for daily deaths from world-o-meter with…
  • A single measure of population prevalence from the Office for National Statistics (ONS).

Now we have more data and so I have produced updated projections for both daily deaths and population prevalence.

Population Prevalence

The ONS now have survey data (link) on the prevalence of people actively ill with COVID-19 in the general population. The data covers 5 weeks:

% testing positive for COVID-19Lower confidence limitUpper confidence limit
26 April to 2 May0.440.250.72
3 May to 9 May0.310.200.50
10 May to 16 May0.220.150.36
17 May to 23 May0.160.100.25
24 May to 30 May0.110.060.19
Data from the ONS

Plotting this on a graph we see a pleasingly decreasing trend.

Right-click and “open in a new tab” to see the graph in more detail.

The population prevalence at the start of June (now) is around 0.1% and the trend is well described by an exponential function which – if the trend continued – would imply a factor 10 reduction in prevalence every 47 days.

PrevalenceDateCases in the UK
1 in 1,000Start of JuneAbout 60,000
1 in 10,000Mid-JulyAbout 6,000
1 in 100,000Start of SeptemberAbout 600
1 in 1,000,000Mid OctoberAbout 60
Projected dates for a given level of COVID-19 prevalence.

We can see the data in more detail if we plot them on a log-linear graph.

Right-click and “open in a new tab” to see the graph in more detail.

This rate of decline is slower than any of us would like, but it is similar to the projection I made a couple of weeks ago.

It suggests that at the start of September the population prevalence of COVID-19 cases might be close to 10 in a million.

Personally, I think this is low enough for life to proceed reasonably normally – albeit with some of our ‘new normal’ behaviours – and probably low enough for schools to operate safely with minimal fuss.

Daily Deaths

Below I have also plotted the 7 day retrospective rolling average of the daily death toll along with the World-o-meter projections.

Right-click and “open in a new tab” to see the graph in more detail.

The predicted rate of decline is similar to the population prevalence projection, falling by a factor 10 in about 50 days.

In my future updates I will use the current World-o-meter projection to gauge whether the death rate is falling faster or slower than we currently hope for.

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.

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.

Corona Virus UK: How will it end?

May 29, 2020

The state of the UK COVID-19 epidemic on day 148 of 2020


Thank you Lydia Denworth for providing me with answers to two questions I didn’t know I wanted answered:

  • Will the Corona Virus Disappear like SARS did in 2003?
  • Where did the 1918 Spanish flu go? 

The answers appeared in a Scientific American article which asked the one question to which we all want an answer:

  • How will the COVID-19 pandemic end?

Will the Corona Virus Disappear like SARS did?

  • SARS stands for Severe Acute Respiratory Syndrome.
  • CoV stands for Corona Virus

There are seven known corona viruses: four circulate widely and cause colds. Both our current pandemic and the SARS epidemic in 2003 were caused by altered strains of corona virus. The original strain was called SARS-CoV and the new strain is called SARS-CoV-2.

The original SARS-CoV was highly virulent but only gave rise to 8098 cases, and 774 deaths. And there have been no new cases since 2004.

This limited spread was achieved by aggressive tactics of quarantining and isolation. But with SARS-CoV people had an advantage.

  • SARS-CoV made people feel obviously unwell – they had difficulty breathing – almost immediately. But they didn’t spread the virus until they were quite severely unwell. This occurred typically one week after obvious symptoms. Thus people sought help before they became infectious.
  • SARS-CoV-2 affects us differently. Although the details are still unclear, it appears people may harbour and spread the virus before developing symptoms that cause them to seek help. Indeed, some people seem to spread the virus without becoming noticeably unwell.

This subtle difference – presumably arising from subtle differences in the interaction between the virus and our cells – has allowed SARS-CoV-2 to spread ahead of our awareness of it.

But viruses cannot exist indefinitely without a host, and so once all SARS infections were stopped and viral transmission ceased, the SARS-CoV virus ceased to exist.

Will SARS-CoV-2 disappear like SARS-CoV? No. It is too late for that. 

So humanity eliminated SARS-CoV by aggressive epidemiology. But what happened to the ‘Spanish’ Flu that killed perhaps 50 million people between 1918 and 1920?

The flu virus is completely different to the corona virus. The strain of flu that caused the 1918 pandemic is called H1N1, and because there was no vaccine, it’s progress around the world was only abated when almost everyone who could be infected, had been – the famous ‘herd’ (or ‘community’) immunity.

After the 1918 pandemic, H1N1 became endemic– circulating widely as a regular winter flu. The virus was not as lethal as in 1918-1919 because of community immunity, and a general tendency of new viruses to become less lethal over time.

As a virus evolves, the most virulent variants of the virus – i.e. those which spread the best –  tend to become more prevalent than more lethal strains. 

So the H1N1 variant evolved for virulence rather than lethality and circulated until the northern hemisphere winter of 1957, when it was eliminated from circulation by a new type of pandemic flu called H2N2.

Eliminated? Yes. The H2N2 variant replaced H1N1! If only we knew how to do that kind of trick.

So what will happen in the end?

In order to get rid of the SARS-CoV-2, we need to stop all active infections of host animals – ourselves and – apparently – bats. 

If we do not invent and deploy a vaccine for SARS-CoV-2, then this virus will become endemic and continue to spread around the world.

In communities like the UK where 93% of the population have not yet been exposed, it will likely represent an ongoing hazard. If exposure to 7% of the population has led to around 35,000 deaths so far, then exposure of the whole population would likely lead to around half a million deaths.

If the population prevalence of the virus is low – at the one sick individual in a million level – then the ongoing outbreak will probably be manageable though ongoing social-distancing, testing, and tracing. This is not where we are and it will be a challenge to reach this level.

We are currently at a prevalence of around 2 to 3 sick individuals in 1000 At this level, with many thousands of new infections every day then there exists the possibility for repeated outbreaks, particularly at large public events.

But over several years, the virus will likely evolve to become less lethal, and it may yet simply fade away like the 1918 pandemic flu – but I would not bet on that outcome.

The wildfire analogy

Viruses are frequently described as ‘spreading like wildfire’. The analogy is apt for understanding both how epidemics grow, but also how they die. 

  • Firstly, in the same way that a flame needs to be actively burning fuel (or smouldering somewhere) in order maintain the possibility of spreading, a virus needs to be actively infecting a host (possibly without symptoms) in order to maintain the possibility of spreading.
  • Secondly, as long as dry foliage exists, there is always the possibility that a wildfire might re-start. Similarly, as long as there exists a susceptible population, then there is always the possibility that an epidemic might re-start. 

Thinking about how a wildfire is contained, firebreaks are used to protect critical areas, but large fires can leap these firebreaks, sending burning embers to isolated locations far from the main fire.

Similarly, we use physical separation and vaccines to suppress the main virus outbreak, but smaller outbreaks can jump our barriers and lurk, ‘smouldering’ in a community.

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.

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.


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.


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


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.


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.



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.

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