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Herd Immunity Revisited – an update

Herd Immunity Revisited – an update

There have been a number of responses to my previous post, most of which have missed the point. Perhaps I didn’t put it clearly enough. So let’s try to clarify it.

The main point is that I am definitely not advocating withdrawal of any attempt to control the epidemic and relying solely on the development of natural herd immunity. It is highly probable that this would lead to hospitals being stretched beyond breaking point (remembering that the policy of this and previous Tory governments in systematically reducing the ability of the NHS to cope with unforeseen crises has played a major part). I say ‘highly probable’, because nothing is certain when it comes to COVID – I suspect the virus has more tricks up its sleeve yet.

I should also say that I am in no way associating myself with the so-called ‘Great Barrington declaration’. At the same time. it does not make sense to automatically reject everything someone says simply because that person has, or is associated with, some unsavoury political views. If Mussolini made the trains run on time (whether that’s true or not), that doesn’t make it a bad idea. Nor does it mean that anyone advocating railway punctuality must be a fascist.

My central point is that lockdown and test-and-trace procedures will not by themselves permanently eradicate the virus. Textbook models of epidemics say that if you get R below 1 and keep it there, the disease will disappear. But one of the central assumptions of that model is that you are dealing with an isolated community. In the absence of herd immunity, the population is still largely susceptible, and any movement of people risks re-introducing the infection.

New Zealand can be considered as an ‘isolated community’, and they seem to have achieved that position – but at the cost of rigorous quarantining of all entrants to the country. A few other islands have done so too. The Isle of Man is making a valiant attempt to do it. Of course Britain is an island as well. But can we consider quarantine for all who come to Britain? Not just asking them to self-isolate, but putting them all into dedicated quarantine hostels for 1-2 weeks? Can you imagine that? It would have to include those coming from Northern Ireland too, which would cause a political storm.

In my view, the real purpose of the current restrictions is, or should be, to slow down the epidemic so that the NHS can continue to cope. And it buys time in the hope that an effective vaccine will become available. In the absence of a vaccine, where will it end? If the restrictions succeed in bringing the 2nd wave under control, my guess is that we would ultimately get a 3rd wave, a 4th wave and so on, until eventually enough people have been infected and we reach the unmentionable herd immunity. In that situation, we would end up with having had the same number of cases, and (unless we get more effective treatment) the same number of deaths. Those taking decisions about the nature and extent of the lockdowns need to balance those objectives against the economic, social, and psychological costs of the lockdowns.

Jeremy Dale

21/10/2020

Herd Immunity Revisited

Herd Immunity revisited

At the start of the pandemic, there was much discussion about the possibility of letting it run its course until ‘Herd Immunity’ was reached. This option was rejected as it was projected to involve perhaps 350,000 deaths and a crisis in hospital admissions. Now, with deaths probably over 50,000, and a ‘second wave’ starting, the option of aiming for herd immunity has resurfaced – more precisely, aiming for herd immunity in the younger age-groups, combined with protection for the most vulnerable sectors of the population. So it seems a good time to have another look at the question.

Background

Statistical models of epidemics predict that, in the absence of any control measures, after an initial exponential rise in the number of cases, the epidemic will start to slow down as the proportion of the population who have already had the disease (and are presumed to be immune) rises, and hence the proportion who are still sensitive declines. Eventually it grinds to a halt because there are no longer enough non-immune people to sustain it. This point is known (rather unfortunately) as herd immunity.

It all hinges on the value of the now infamous parameter called R. For COVID-19, R is thought to be somewhere between 3 and 4, in a wholly susceptible population, in a country like the UK. That is, one infectious individual will, on average, infect 3-4 others. The point at which herd immunity kicks in (the Herd Immunity Threshold, HIT) can be estimated from the initial value of R, so if R=3, then HIT is about 67% (or 2/3). That’s about 40 million cases.

To calculate the number of expected deaths, we need to know how many of those will die – the case fatality rate. That is commonly put at about 1% (on average). 1% of 40 million is 400,000 (which is more or less where that 350,000 figure comes from).

The value of R is not just down to the nature of the virus. It is also influenced by the probability of making an ‘effective contact’ – that is a contact between an infectious person and a non-immune one, which is in turn affected by a number of factors such as how long you remain infectious, as well as how many people you come into contact with while you are infectious. This will depend on where you live; someone living in a remote area will contact very few people compared to one in a big city. A national value of R is a very rough measure of progress as it is an average value over areas with widely different real values.

The likelihood of an effective contact will also depend on your personal behaviour, especially the extent to which you go and mix with others. This is where the lockdown measures come in. They are an attempt to alter people’s behaviour so they will contact fewer people, and hence drive down the value of R.

So what?

Suppose the restrictions succeed in driving down the value of R to below 1, and keeping it there, the model tells us that each infectious person is infecting less than one other person, and hence the disease will die out, even without achieving herd immunity. And we’ll suppose that at this point, say 20% of the population have been infected (and hence are assumed immune). We would now have no cases, but 80% of the population is still non-immune. Is that the end of the story?

If we were living in complete isolation from the rest of the world, it would be. But we are not. All it needs is for one infected person to enter the country from an area where the disease is still rampant and away we go again. New Zealand is in just this situation, and they are attempting to keep it out by quarantining all those entering the country (which must devastate their tourism industry). But it is unimaginable for the UK to attempt to do this.

Furthermore, although after the first wave of infections there was a very substantial drop in the number of cases (presumably due to the restrictions, or some of them anyway), the disease did not disappear completely. There were enough cases continuing to be able to re-seed the epidemic once the brakes were taken off, so the second wave was inevitable. If the new restrictions now coming in succeed in controlling the second wave, we can confidently assume the same will happen again.

What this tells us is that if we don’t achieve herd immunity, we will have to carry on with some form of lockdown indefinitely (at least until a reasonably effective vaccine is available).

So we need to look again at the herd immunity strategy, and the assumptions that led us to reject it initially. In particular, how far have we already gone in that direction – in other words how many people have actually been infected? The limitations of testing means that it doesn’t tell us that. One way to estimate it is by looking at the number of deaths. Let’s call that 60,000 (a bit higher than the data from death certificates). If the case fatality rate is 1%, that implies a total of 6 million infections so far; in other words, about 10% of the population have now been infected at some stage. If the fatality rate is lower than that (I have seen estimates from elsewhere that put it as low as 0.3%), then the number of infections could be much higher, possibly up to 30% of the population. If you were to do this calculation in earnest, you would need to allow for the number of deaths in the elderly or other highly vulnerable groups (with a much higher fatality rate).

Alternatively, a more direct way, is to assess the frequency of SARS-CoV-2 antibodies in the population. ONS do sample surveys to measure this, and the latest figures I’ve seen put it at about 6%. However, this does assume that everyone who had been infected at some stage produces enough antibody to be detected by the test.

If we take somewhere in the region of 10% as the proportion who have been infected, that is still way short of the 67% that we think is needed for herd immunity. However, we’re looking at overall figures for the whole country, while COVID has affected some places much more than others. Trying to unravel that gets complicated, especially as those places with more cases have a higher initial value of R, and hence require a higher level of herd immunity. But it is tempting to wonder why London has not seen anything like the same level of 2nd wave (as yet).

However, although we may still have a way to go before getting herd immunity, is there any alternative? Of course, if a vaccine emerges (even a partially effective one), it would change the situation drastically. Without that, are we faced with having restrictions indefinitely? It may be that all that would achieve is to prolong the epidemic, but smoothing it out so that the NHS doesn’t get overwhelmed. In other words, we would get the same number of cases, and deaths, but over a longer time.

One alternative that is being canvassed is to withdraw restrictions and allow the epidemic to run its course, while, at the same time, providing better protection for those more vulnerable, especially in care homes. In that way, we could build up herd immunity in those who are very much less likely to suffer serious effects, which in turn would protect the most vulnerable. This is often caricatured as locking away all the elderly and sick people and throwing away the key. But it doesn’t have to mean that. We could, for example, provide much better support for care homes – not just PPE for the staff (important that it is) but also in installing facilities, such as screens, that would allow safe visiting. And we would need to make sure that those who were isolating at home would also receive better support, not just in providing food parcels, but again devising ways in which they could safely receive visitors.

The final verdict must be that unless and until we get a vaccine, herd immunity (however it is achieved) is the only way in which this epidemic will cease.

COVID-19 – a bit of perspective: update

An update

According to ONS, in the week up to Sept 11th, there were 9,215 deaths from all causes in England. Of these, COVID-19 accounted for 97 deaths – that is about 1% of the total. Of course, we would expect that figure to rise as the number of cases increases. For the whole period of the epidemic (up to Sept 11), COVID deaths (52,482) account for about 12% of the total number of deaths (434,618) in England and Wales..

If we assume a case fatality rate (the number of deaths as a percentage of the number of cases) of 1%, this means that just under 9% of the population have been infected.  But we don’t know the case fatality rate for sure; I have seen estimates that put it as low as 0.3%. If that is true, then the number who have been infected (England and Wales) would be as high as 17.5 million, or 29% of the population.  That would mean, given the highly uneven spread of cases, that there would be some areas that would, at some point during the ‘second wave’, approach the level required for herd immunity to kick in (usually taken as about 60%).

Jeremy Dale 25/9/20

COVID-19 – a bit of perspective

Every death is a tragedy for those affected. Especially so for COVID, where someone may die in isolation, unable to see, or be seen by,  their loved ones. In no sense do I want to diminish that – and if you have been affected by the virus you may not want to read on. But in the midst of all the publicity about COVID, I feel it is necessary to try to put it into perspective.

First of all, let’s look at the data for COVID deaths. This is very confusing. The Government dashboard (1 August) puts it at 46,193 in the UK. This is the number who have died having had a positive test result. This has been much criticised, as it would seem to mean that even if you get run over by the proverbial bus, having been tested positive months ago, you are still counted as a COVID-related death. On the other hand, if you die from COVID but have never been tested (or the test didn’t work), you wouldn’t be counted.

If you look at the data from the Office of National Statistics (ONS), you get a different figure,  50.800, in England and Wales only. This comes from death certificates, and is the number of times COVID was mentioned (even if other causes such as pneumonia were also mentioned). I’ll stick with the ONS figure, mainly because I want to compare it with other data from ONS.

So, 50,000 deaths. That’s a lot of tragedies. But death is a part of life. During the period of the epidemic, 245,000 people have died from all causes – so that’s getting on for 200,000 people have died from something other than COVID. And during each of the last five weeks, more people have died from what is recorded as Influenza/pneumonia than from COVID.

Another way of looking at the impact of COVID is to consider the excess deaths – that is the number of people who have died from any cause, compared to the average number who died in the same period over the last five years. This shows that since the epidemic started there have been over 53,000 excess deaths. That measure includes the possible indirect effects of COVID, e.g., people who didn’t get appropriate treatment in time. If we look at the weekly breakdown of excess deaths, we see that during the last five weeks it has been negative – that is, fewer people are dying than expected. The likely reason for this is that one effect of COVID has been to cause the death of some people who would otherwise have died soon anyway.

Historical comparisons

The current crisis has highlighted the fact that we are no longer used to people dying in large numbers from infective diseases. Medical advances, including antibiotics and vaccines, coupled with improvements in nutrition, housing, public health and other environmental issues, have in general made such diseases of historic interest only, at least in countries like the UK. (This is not of course true for most of the world, where diseases such as malaria and tuberculosis are causing death and suffering on a large scale – in low income countries, communicable diseases represent 5 of the top 10 causes of death).

A look at the death statistics (from ONS) for 100 years ago (1915) illustrates the point. In that year, there were 66k deaths from pneumonia/bronchitis and 39k deaths from tuberculosis. We can add others – 13k deaths from measles. 5k each from diphtheria and flu (not an epidemic year), 4k from whooping cough and nearly 2k from scarlet fever.

In the more distant past, there are numerous examples of devastating infections. The Black Death (1381) is thought to have killed a third of the population. In the nineteenth century, there were repeated epidemics of cholera, with tens of thousands of deaths, and tuberculosis was rampant (at its height, causing a third of all deaths).

In more recent times, the best comparison is with pandemics of influenza. (Technical note: Influenza viruses are classified by their H and A antigens, the most common type being H1N1. Various H1N1 strains are similar but not identical in both, so you get a degree of cross-immunity, while another type say H2N2 differs in both and there is no cross-immunity between them. Major pandemics usually occur with a virus that has ‘shifted’ to different H and N types)

In 1957-58 there was a pandemic of so-called ‘Asian flu’ (H2N2), which caused some 20-30k deaths in the UK. Then in 1968-69, we had an H3N2 strain (labelled ‘Hong Kong’ flu) for which the estimates of the number of UK deaths go up to 80k. In neither case was the official response anything like what we are currently seeing with COVID-19. And the media managed to find plenty of other news to cover.

More recently, there was some concern about ‘swine flu’ (2009). The incidence rose to about 110k cases per week in July, before dropping off, and then re-emerging in the autumn to about 84k cases per week in October. However, mortality was low (<1,000 deaths in UK), probably because this was an H1N1 strain, and older people had already encountered H1N1 strains and so had significant immunity to it.

Why all the fuss?

Why is it that fifty years ago we could face a disease that caused up to 80k deaths, not exactly with equanimity but at least without the massive sacrifices that we are currently making for a disease of (apparently) similar magnitude? Of course, we have to recognise that without the control measures it might have been much worse. Based on what was known about the disease, the initial assessment was that, if left unchecked, the disease would spread until Herd Immunity was achieved, and that would happen when about 60% of the population had been infected. Assuming a case fatality rate of 1%, that implied something like 350,000 deaths, which was deemed unacceptable. Of course we will never know if that would have happened, but a comparison with other countries is interesting. We hear a lot about the numbers of deaths in the USA and Brazil, but if we look at the numbers of deaths per million population, we are still some way ahead of either of them (UK 680, USA 477, Brazil 440) – although I am well aware of the dangers of reading too much into such comparisons, given the different methods and reliability of reporting deaths. But superficially, it could mean that our lockdown didn’t have much effect, and the original estimate of 350,000 deaths was over the top.

I’m not saying that we should all ignore the advice, and go out and party. But let’s keep a sense of perspective. At the individual level, unless you are in an extremely vulnerable category, there are plenty of other ways of dying that we don’t bother too much about. But collectively, we still have a duty to try to limit transmission so as to protect those who are more vulnerable. Above all, don’t panic!

Jeremy Dale

2 August 2020

Moonshine Project

Is it a good idea to regularly test the whole population for infection with SARS-CoV-2?

Superficially, you might well say the answer is ‘Yes, obviously’. But I want to look at it in more depth.

First of all, obviously, there are the practical considerations. The current system, fragmented as it is (some would say deliberately fragmented between the private and public sector), is proving to be quite unable to cope with testing those who really need it. And the tracing aspect is even worse. Remember when you hear the figures quoted, e.g., 70% of infections are detected, and 70% of contacts are traced – that is 70% of 70%, or 49%. So even with the Government’s claims, only about half of potential contacts are traced. And it is far too slow – several days to get the test result, and several more days (often longer) to reach the contacts, who thus may have been spreading the disease for days before being told to isolate,

Secondly, it depends on technology that doesn’t yet exist. There is much talk about rapid tests that are being introduced. These are antibody tests, which only tell you whether someone has been infected at some time in the past, not whether they are currently infected, Antibody tests don’t give a positive result until the infection is, in most cases, over.

Leaving the practicality aside, let’s assume that somehow we do have a test that can be easily and rapidly done for vast numbers of people. Would it be a good idea then, to screen the whole population?

To answer that question, we need to look at some concepts related to the test. I should clarify that what I mean by ‘test’ is what happens in the laboratory with the sample you have provided. The other parts of the process – taking the sample, transmitting it to the lab, and reporting the results – all have their problems, but I’m not considering those.

No laboratory diagnostic test is perfect. Biological systems are very complex, and all sorts of things can lead to a ‘wrong’ result. This can mean that someone who is infected gives a negative result (a ‘false negative’). For example, there might be something in the sample that interferes with the test process. The ability of the test to detect real positives is referred to as the sensitivity, which is defined as the number of positives detected divided by the number of true positives.

The other side of the coin is the specificity, which roughly means the ability of the test to correctly identify someone who is not infected. This is defined as the number correctly identified as negative divided by the number who are really not infected. This gives us a measure of how often we would get a false positive – i.e., a positive test result for someone who does not have the disease.

Now we can look at what this means in reality. Let’s assume we have a test that is 99% sensitive and 99% specific. That would be regarded as a really good test. And let’s assume we have a prevalence of 1 in 1,000. So, in a population of 100,000, there would be 100 cases, and the test would detect 99 of them. That’s not bad. The crunch comes with the specificity. In this situation, the test would return a positive result for 999 people who do not have the disease (false positives). In other words, there would be about 10 false positives for every correctly identified positive. If we scale that up to 60 million people, there would be nearly 600,000 people who would be told they were infected when they weren’t. Would they all have to isolate themselves? And even thinking about contact tracing on that scale gives me a headache.

These considerations apply to all occasions when you are screening random samples for some relatively rare event, whether it’s screening donated blood for an infectious agent such as HIV, or mass screening for cancer. The standard way of dealing with it is to use two independent tests. So, you take all the samples that gave a positive result in the first test and re-test them, with a different test. (It has to be a different test as the reason for the ‘wrong; result might be inherent in the sample). If you did that, with the above example, then after re-testing all the positives from the first test, you would find that fewer than 10% of the positives would now be false positives.

In effect this is what happens when you use a test to confirm a clinical diagnosis, or if you are applying a COVID-19 test to people who have symptoms. The clinical picture is the first test, giving a group of people who are much more likely to have the disease than the general population is.

Is a two-step procedure feasible? It could be argued that the first step could use the hitherto unknown and entirely conjectural rapid test, and the positive samples submitted to the existing PCR-based test – but only if this hypothetical new test was something entirely different. And it would still demand adding an additional 600,000 samples to the existing testing workload. Since that system is currently unable to meet the present demands, this seems unlikely.

If you would like to see the calculations I have used, and play around with them, send me an email and I’ll send you the spreadsheet.

Jeremy Dale

20 Sept 2020

COVID-19 – a bit of perspective

An update

According to ONS, in the week up to Sept 11th, there were 9,215 deaths from all causes in England. Of these, COVID-19 accounted for 97 deaths – that is about 1% of the total. Of course, we would expect that figure to rise as the number of cases increases. For the whole period of the epidemic (up to Sept 11), COVID deaths (52,482) account for about 12% of the total number of deaths (434,618) in England and Wales..

If we assume a case fatality rate (the number of deaths as a percentage of the number of cases) of 1%, this means that just under 9% of the population have been infected.  But we don’t know the case fatality rate for sure; I have seen estimates that put it as low as 0.3%. If that is true, then the number who have been infected (England and Wales) would be as high as 17.5 million, or 29% of the population.  That would mean, given the highly uneven spread of cases, that there would be some areas that would, at some point during the ‘second wave’, approach the level required for herd immunity to kick in (usually taken as about 60%).

Jeremy Dale 25/9/20

COVID-19 – a bit of perspective

Every death is a tragedy for those affected. Especially so for COVID, where someone may die in isolation, unable to see, or be seen by,  their loved ones.

In no sense do I want to diminish that – and if you have been affected by the virus you may not want to read on.

But in the midst of all the publicity about COVID, I feel it is necessary to try to put it into perspective.

First of all, let’s look at the data for COVID deaths. This is very confusing. The Government dashboard (1 August) puts it at 46,193 in the UK. This is the number who have died having had a positive test result. This has been much criticised, as it would seem to mean that even if you get run over by the proverbial bus, having been tested positive months ago, you are still counted as a COVID-related death. On the other hand, if you die from COVID but have never been tested (or the test didn’t work), you wouldn’t be counted.

If you look at the data from the Office of National Statistics (ONS), you get a different figure,  50.800, in England and Wales only. This comes from death certificates, and is the number of times COVID was mentioned (even if other causes such as pneumonia were also mentioned). I’ll stick with the ONS figure, mainly because I want to compare it with other data from ONS.

So, 50,000 deaths. That’s a lot of tragedies. But death is a part of life. During the period of the epidemic, 245,000 people have died from all causes – so that’s getting on for 200,000 people have died from something other than COVID. And during each of the last five weeks, more people have died from what is recorded as Influenza/pneumonia than from COVID.

Another way of looking at the impact of COVID is to consider the excess deaths – that is the number of people who have died from any cause, compared to the average number who died in the same period over the last five years. This shows that since the epidemic started there have been over 53,000 excess deaths. That measure includes the possible indirect effects of COVID, e.g., people who didn’t get appropriate treatment in time. If we look at the weekly breakdown of excess deaths, we see that during the last five weeks it has been negative – that is, fewer people are dying than expected. The likely reason for this is that one effect of COVID has been to cause the death of some people who would otherwise have died soon anyway.

Historical comparisons

The current crisis has highlighted the fact that we are no longer used to people dying in large numbers from infective diseases. Medical advances, including antibiotics and vaccines, coupled with improvements in nutrition, housing, public health and other environmental issues, have in general made such diseases of historic interest only, at least in countries like the UK. (This is not of course true for most of the world, where diseases such as malaria and tuberculosis are causing death and suffering on a large scale – in low income countries, communicable diseases represent 5 of the top 10 causes of death).

A look at the death statistics (from ONS) for 100 years ago (1915) illustrates the point. In that year, there were 66k deaths from pneumonia/bronchitis and 39k deaths from tuberculosis. We can add others – 13k deaths from measles. 5k each from diphtheria and flu (not an epidemic year), 4k from whooping cough and nearly 2k from scarlet fever.

In the more distant past, there are numerous examples of devastating infections. The Black Death (1381) is thought to have killed a third of the population. In the nineteenth century, there were repeated epidemics of cholera, with tens of thousands of deaths, and tuberculosis was rampant (at its height, causing a third of all deaths).

In more recent times, the best comparison is with pandemics of influenza. (Technical note: Influenza viruses are classified by their H and A antigens, the most common type being H1N1. Various H1N1 strains are similar but not identical in both, so you get a degree of cross-immunity, while another type say H2N2 differs in both and there is no cross-immunity between them. Major pandemics usually occur with a virus that has ‘shifted’ to different H and N types)

In 1957-58 there was a pandemic of so-called ‘Asian flu’ (H2N2), which caused some 20-30k deaths in the UK. Then in 1968-69, we had an H3N2 strain (labelled ‘Hong Kong’ flu) for which the estimates of the number of UK deaths go up to 80k. In neither case was the official response anything like what we are currently seeing with COVID-19. And the media managed to find plenty of other news to cover.

More recently, there was some concern about ‘swine flu’ (2009). The incidence rose to about 110k cases per week in July, before dropping off, and then re-emerging in the autumn to about 84k cases per week in October. However, mortality was low (<1,000 deaths in UK), probably because this was an H1N1 strain, and older people had already encountered H1N1 strains and so had significant immunity to it.

Why all the fuss?

Why is it that fifty years ago we could face a disease that caused up to 80k deaths, not exactly with equanimity but at least without the massive sacrifices that we are currently making for a disease of (apparently) similar magnitude? Of course, we have to recognise that without the control measures it might have been much worse. Based on what was known about the disease, the initial assessment was that, if left unchecked, the disease would spread until Herd Immunity was achieved, and that would happen when about 60% of the population had been infected. Assuming a case fatality rate of 1%, that implied something like 350,000 deaths, which was deemed unacceptable. Of course we will never know if that would have happened, but a comparison with other countries is interesting. We hear a lot about the numbers of deaths in the USA and Brazil, but if we look at the numbers of deaths per million population, we are still some way ahead of either of them (UK 680, USA 477, Brazil 440) – although I am well aware of the dangers of reading too much into such comparisons, given the different methods and reliability of reporting deaths. But superficially, it could mean that our lockdown didn’t have much effect, and the original estimate of 350,000 deaths was over the top.

I’m not saying that we should all ignore the advice, and go out and party. But let’s keep a sense of perspective. At the individual level, unless you are in an extremely vulnerable category, there are plenty of other ways of dying that we don’t bother too much about. But collectively, we still have a duty to try to limit transmission so as to protect those who are more vulnerable. Above all, don’t panic!

Jeremy Dale

2 August 2020

 

COVID-19: Airborne transmission?

COVID-19: Airborne transmission?

Some of you may have been as confused as I was by the recent reports suggesting that the possibility of airborne transmission of SARS-CoV2 has been neglected. You would be forgiven for thinking that the airborne route is what we’ve been talking about all along, and that it is the main route of transmission. That’s what masks and distancing are all about. This is an attempt to straighten out the issues.

Basic principles

When we cough or sneeze, or, to a lesser extent, talk or even just breathe, we eject small droplets of saliva and mucus. A sneeze may produce thousands of these, while a cough may yield only a few hundred. For talking, or singing, it will depend on the consonants – f, b, p, t and s are especially good at producing droplets (I am indebted to Cedric Mims in The Pathogenesis of Infectious Disease for the observation that most abusive words in English start with one of these consonants!). If we are infected with a respiratory tract pathogen, such as SARS-CoV2, then some of these droplets may contain virus particles. I’ll come back to that later.

What happens to those droplets? That depends on their size. The largest ones (1mm or more) will fall to the ground (or some other surface) within a few metres or less. With the smaller ones, because they have a large surface area relative to their volume, the water content will evaporate rapidly, resulting in tiny particles (‘droplet nuclei’) less than 5 micrometres in size (a micrometre is a millionth of a metre, or a thousandth of a millimetre). These can remain airborne virtually indefinitely. It is the potential of these particles to transmit the disease that is the focus of the current discussion. This is sometimes referred to as ‘aerosol transmission’ to distinguish it from transmission by large droplets.

Some unanswered questions

In order to assess the significance of the potential risk posed by these tiny particles, we need to consider the following factors:

– the likelihood that they carry the virus

– how many virus particles they carry

– how long will the virus remain able to establish infection

– how are they distributed in the air

– How many virus particles are needed to cause an infection (the infective dose).

Most of these are unknown; we’re just guessing, partly based on experience with other viruses. Let’s fill in some details.

Will the particles contain virus particles, and how many?

This depends on another unknown, the viral load, or more specifically the number of virus particles shed by someone infected. One of the main factors limiting our knowledge here, and elsewhere, is that almost exclusively the assays are based on detection of viral RNA rather than viable virus particles (which are much more difficult to measure).

Leaving that question on one side, it is intuitively obvious (and probably true) that the larger droplets are more likely to contain virus particles than smaller ones, and similarly are likely to have more virus in them. That’s just on a statistical basis. You should also consider the size of the virus. A single coronavirus, including the spikes, is about 130 nanometres (nm) in diameter (one nanometre being a thousandth of a micrometre). So if you put 7 or so viruses side by side, that would span the diameter of a one micrometre droplet. Without doing the detailed calculation, it can be estimated that the maximum capacity of the largest of these persistent airborne droplets (say 5 micrometres) might be of the order of 100 virus particles, if they can be tightly packed. And many of the droplets will be much smaller, containing no more than a few viruses. This will be relevant when we look at the infectious dose later.

How long does the virus remain infectious in small droplets?

Another unknown, and here the RNA assay is of no help at all. RNA will remain long after the virus itself is ‘dead’. But it is likely that it will be of limited duration due to drying – and, especially in the open air, the effect of UV light.

How are the droplets distributed?

This is a bit easier to answer. For the larger droplets, which are essentially transmitted directly from the source to the subject, the likelihood is dependent on the distance separating them, and more or less to the square of that distance (as it can go to either side of you). If the smaller droplets are distributed throughout the air-space, it will be related to the size of the room you are in. If you have a lot of people in a small, low ceilinged, room, then the risk may be considerable. If the room is larger it will be much less so, especially if the room is well ventilated. And of course if you are outside, the risk virtually disappears.

How likely are you to be infected?

This depends on the biggest unknown of them all, the infectious dose (i.e., how many virus particles do you need to inhale in order to catch the disease?). This varies a lot from one disease to another, from a few hundred up to millions. Because we have a variety of non-specific mechanisms protecting us against invading microbes, very few diseases have infectious doses less than a few hundred – it is often said that tuberculosis can arise from a single bacterium penetrating as far as the lungs, but that is exceptional (and a bit dubious!). For the original SARS virus, the infectious dose has been estimated as a few hundred (although this is not much more than a guess, and it may be higher), so it is often assumed that this will apply to SARS-CoV2 as well. If we combine that estimate with the previous discussion, recognising that each of these tiny droplets is likely to contain only a small number of virus particles, we would have to inhale dozens or hundreds of such particles. Potentially, this could happen in a small, ill-ventilated room if there was someone shedding large numbers of virus, but my conclusion is that this is likely to have a comparatively small effect on the overall transmission of the virus, compared to the risk of more direct transmission by larger droplets.

Jeremy Dale

10 July 2020

World-beating?

World-beating?

Johnson likes to talk up the UK performance in dealing with COVID-19. But strangely he doesn’t consider one statistic that shows the UK competing strongly for the ‘world-beating’ title. If we ignore San Marino, that title goes to Belgium, but with the UK in second place (here I ignore Andorra, with my apologies to both countries) – and closing.

We hear a lot about the numbers of deaths in various countries, and how USA and Brazil are leading the field- but to get a true picture we need to relate this to the population size, as deaths per million inhabitants, a parameter known to epidemiologists as the ‘death rate’. Let’s look at some data (as at 13 June).

Belgium has recorded 841 deaths per million. For the UK the figure is 621.

Spain and Italy are close behind (581, 566 respectively).

Some others for comparison: Sweden 482, France 452, Ireland 354, USA 352, Brazil 204, Germany 106. Of these, USA and Brazil are both likely to move up the list.

I should add that all of these figures are somewhat suspect, some more so than others, as practices vary between countries, for example in whether they are COVID-confirmed or merely suspected, and how assiduous they are in ascertaining COVID-related deaths in the community.

How did we get to the unenviable position of being (almost) world-beating?

The UK Government has done a lot of things wrong (or failed to do the right things). I’m not going to attempt a complete list, but a few examples will suffice.

It starts several years ago. There were warnings from at least two ‘exercises’ that we were ill-prepared for a pandemic – notably, but not solely, in the inadequacy of the stockpiles of PPE. These warnings were not acted upon. I suspect that the government was influenced by the ‘just in time’ business model, which holds that stockpiles are inefficient. This model failed spectacularly as it doesn’t deal with a situation when circumstances change suddenly (as supermarkets also found out).

Other problems arose from the repeated reorganisation of the infection control systems. At one time, each hospital had its own diagnostic lab, and each local authority had well-organised arrangements for monitoring and dealing with outbreaks of infectious diseases, including experienced teams of contact tracers. Much of this was dismantled and centralised, and what was left has been largely ignored by the government. Hence people having to travel considerable distances to be tested and it taking several days to get the results back.

Then we come to the lack of action at the early stages of the pandemic. Warnings were there in January, becoming more serious in February. The government did nothing until well into March. No controls on passengers coming to the UK, not even temperature checks. Now we hear that there were at least 1300 separate introductions of the virus to the UK.

They also failed at that stage to ramp up the provision for testing and contact tracing, so that it quickly became overwhelmed when the outbreak started in earnest, and had to be abandoned. It could have made a vital difference at that stage.

They were very slow to stop large gatherings of people – including the rugby international at Twickenham (7 March), the Cheltenham Races (10-13 March) and the Atletico Madrid match at Anfield (11 March). They maintain that the scientific advice was that these events were low risk – and it could be that while people were sitting in the stands watching, the risk was less than for people in a crowded pub. But what about travel to get there? What about the bars at the event? And in the pubs afterwards?

Even after those events, with the warnings becoming clearer and clearer, it took them another two weeks to impose a lockdown.

A large part of the blame must lie with Johnson himself – first of all his refusal to engage with the issue during January and February, and then, well I can’t blame him for being ill, but he seems to have established a cabinet without anyone able to take charge in his absence. And to cap it all, his failure to deal with Cummings after his flagrant flouting of the lockdown has created a situation where large sections of the populace no longer have the respect for the advice that is necessary for maintaining control during the easing of the lockdown.

I could go on – the refusal to co-operate with the EU over the supply of PPE and ventilators (was this a dogmatic antagonism to anything ‘European’?), the hesitation and vacillation over any changes, and then imposing them suddenly without warning, and without consultation with those who would be most affected – notably the fiasco over the re-opening of the schools, plus the multitude of ever-changing ‘guidance notes’, and the proposal to change the distancing rules – will they, won’t they? Who knows? But enough is enough.

 

Jeremy Dale

15/6/20

 

Am I a Racist?

Am I a Racist?

The killing of George Floyd, and the world-wide reaction to it, has brought the issue of racism to the fore once again. So this is a good time to think a bit about what we mean by ‘racism.’

The dictionary definition starts with “belief in the superiority of a particular race”. Leaving on one side the absence of any scientific meaning to the term ‘race’ in this context, this definition is rather an extreme position; we really need something broader. The second definition in my dictionary – “antagonism towards other races” –gets nearer to the current issues, but I maintain is still inadequate. I would certainly not admit to being a racist on either of those definitions.

Basically I don’t like the terms ‘racist’ and ‘racism’. I would prefer to redefine my starting  question as ‘Am I racially prejudiced?’ To which, if I am honest, the answer must be ‘Yes’. That needs some explanation.

I think, as a white person living in a society such as Britain that is historically ‘white’, (and still remains dominantly white, politically, economically and culturally), a degree of racial prejudice is inescapable. I say nothing about how someone from another ethnic background would feel; how could I possibly know? The challenge that we face is to recognise, and try to deal with, that prejudice.

One example. I’m walking along a street and I see ahead of me a group of people largely blocking the pavement. Do I a) continue and hope they make way for me to pass. b) step out into the road to pass them, or c) cross over to the other side of the street. I know that my instinctive reaction would be different if they were black. I know nothing else about them; I have no reason behind my reaction. I am pre-judging the situation – which is prejudice. You can extend this scenario to other forms of prejudice – contrast my likely behaviour if they were young males as opposed to elderly women.

Another, real, situation. When I was a University lecturer, many years ago, students had to put their names on the front of their exam papers. Some of us thought this was not good practice, and we argued (eventually successfully) for anonymous marking. There was opposition to this – some of my colleagues were actually offended by the implication that their marking might be affected by knowing who the student was. They said they weren’t prejudiced. I knew I could be, and so I always tried not to look at the cover page. But after I had given a mark, I sometimes thought, when I did see who the student was, ‘That can’t be right. She’s done much better than I expected.’ And I was tempted to go back and re-mark it.

So, yes, I admit to prejudice. And I come from a Quaker family background, with deep roots opposed to all forms of prejudice. Hence my contention that all (or at least all white people in a society such as ours) must also be prejudiced. The people who worry me are those who deny their prejudice. Until you recognise it, you cannot deal with it.

On a larger scale, this applies to organisations and institutions as well. To refer to an organisation as ‘institutionally racist’ does not mean, as it is often taken to mean, that every individual in that organisation is overtly racist. Rather it means that the organisation has failed to recognise the possibility of racial prejudice inherent in its practices and procedures, and by failing to recognise them it has failed to deal with them.

How does this relate to the killing of George Floyd – and very many other similar incidents, in this country as well as the USA and elsewhere? I have to resort to the rather hackneyed comparison with an iceberg. The tip of an iceberg showing above water only exists because of the very much larger mass of ice out of sight beneath the water. If you tried to cut the tip off, the iceberg would float higher in the water. In other words, it is not sufficient simply to campaign against such incidents of racial violence. Nor is adequate to tackle the inequalities in society. These actions are necessary, but incomplete. To banish ‘racism’ we have to work to eliminate all forms of racial prejudice – in our institutions and organisations, and in ourselves. This requires all of us to recognise the existence of our prejudices, and take appropriate action to counter them..

Jeremy Dale

6 June 2020.

 

 

Stay alert – a guide

Stay alert – a guide

As the ‘English’ government seems to be unable to explain clearly what the new regulations mean, for those who live in England, I thought I would help them out a bit. This is not based on scientific advice, or anything else.

Stay alert.  Obvious, but difficult to do. I find myself nodding off by the end of the day, and eventually I confess I have to give up and go to bed. I hope nobody reading this shops me. I don’t want the police coming round in the middle of the night and asking complicated questions to test how alert I am.

Visiting family and friends. You can now do this, as long as they don’t live in Wales or Scotland. Except they changed their minds; Johnson now says it’s only ‘one on one’.  But there’s two of us, so if we visit family we can only visit one member each. After a while, we can swap over. And it has to be in a public place (not in their garden*).  If, while I’m talking to one friend (A), another friend (B) comes by, I can start talking to B only if A backs off. If we all stay 4 metres apart then that’s OK.

*If you live in Chatsworth, your garden is public. so that’s OK. I’m thinking of declaring my garden a “public space” so I could have friends visiting me.

Travel. You can now travel as far as you like, as long as you don’t stray over the border. But everything will be shut when you get there, so take your own food – but if you end up in Wales, you would have to eat it standing up because otherwise it would be a picnic, which is not allowed. And take a sunhat, and cover yourself up well, otherwise you would be accused of sunbathing.

Quarantine. If you enter the UK (or do they mean England?) by air, you will have to go into quarantine for 14 days. No, that’s changed. Now it applies however you arrive. No, that’s changed too – it doesn’t apply to entry from Ireland or France. If you come from anywhere else, you have to go to France first and then come to England.

(At the risk of sounding serious, why do this now – when we have more cases than most other countries in Europe – and not 3 months ago when we had few cases. And why 14 days? The median time between infection and symptoms is 5-6 days.)

Garden centres. Your best bet is to find one in Wales, close to the border, and go there. Technically, you’re not allowed to drive far in Wales, but if it’s close to the border the police might not notice.

Other cross-border activities. Take care (be alert!) when doing anything close to the border in case you stray across. This includes walking in the Cheviots or the Black Mountains. It also includes any golf courses that cross the border, where you can only play those holes that are in England. If your tee shot is wayward, you will lose the ball.

Face covering. Recommended to be used in enclosed spaces, but not proper face masks which are needed elsewhere. Niqab is suitable but beware of being mistaken for a letterbox. (Strange that some countries ban face covering but also make it mandatory!)

Swimming is allowed, outdoors. So rivers are fine, but be careful in parts of rivers like the Tweed and Wye. If you stray too far across the river, you will find yourself in Scotland or Wales. which is not allowed. See Cross-border activities.

Jeremy Dale

12 May 2020

 

COVID-19: Contact tracing

COVID-19: will contact tracing work?

It’s widely said that testing and contact tracing (using a smartphone app) is the key to the control of COVID-19. But it is not necessarily that simple; there are several unknowns that are worth thinking about.

The textbook example that underpins much of the thinking about this issue is the eradication of smallpox. The later stages of that campaign relied on the early detection of cases and the vaccination of “contacts” (in this case, everyone within a certain area). There are several factors underlying the success of that strategy.

The most obvious is the availability of an effective vaccine. We don’t have that (yet?) for COVID-19.

Secondly, the symptoms of smallpox were obvious and distinctive. There was no need for a complex and time-consuming test to identify a case. In the final stage, in remote areas of Ethiopia, one person in each village was trained to spot, and report, cases, so the vaccination team could respond quickly.

A third important factor is that smallpox is not infective until symptoms appear. Here there is considerable uncertainty in the comparison with COVID-19. There is circumstantial evidence that transmission may occur from pre-symptomatic individuals (i.e., those who subsequently develop symptoms) and possibly also from asymptomatic people (who never develop recognisable symptoms) – although probably to a lesser extent than from those who have symptoms. But we don’t really know, and if it happens to a significant extent it could reduce the effectiveness of a contact tracing strategy. On the other hand, if R is less than one for pre-symptomatic/asymptomatic individuals, then it might not matter.

The comparison with smallpox does have one favourable factor. Both diseases have a relatively low R0 value (2-4)*. This is a marked contrast with another textbook example – measles, where the R0 value is much higher (15-20 is often quoted). Measles also provides another contrast, in that the initial disease is an inconspicuous respiratory tract infection. This is the infectious stage. The typical symptoms come later (they are an immunological response to the virus), and by that stage the patient is not infectious. The high R0 value would make a contact tracing strategy extremely difficult; infectivity before detection makes it effectively impossible.

*A digression to clear up a point that often causes confusion. For epidemics in general, R0 (the basic reproduction rate) is the value of R at the start of a new epidemic, when everyone is susceptible. As the epidemic progresses, and the number who have had the disease (and become immune) increases, the value of R (the actual reproduction rate) declines. For COVID-19, we are largely looking at the effect of control measures rather than the number of those who have become immune; nevertheless it is simpler to refer to this as an effect on R rather than R0.

Before getting back to the point – will contact tracing work in enabling a relaxation of the lockdown while still keeping R below 1? – we need a more subtle interpretation of R. It is an average value across the whole population. If R is very low for some people and much higher for others, you could still get an average value of R <1 even if there is a subpopulation that is spreading the virus quite effectively. If this is geographical (a rural-urban distinction for example) it will show up quite readily (and already does). But if it applies to different groups within say a major city, it is not so easy to see.

Furthermore, although a value of R<1 is (rightly) regarded as a significant point in predicting a decline in the epidemic, it is not an absolute objective. The further it can be reduced, the quicker the epidemic will die out (as well as countering the possibility of a sub-population of spreaders.

Now we can think more clearly about contact tracing. Firstly it depends on the relationship between infectivity and symptoms. Assuming, for the moment, we will not be undertaking massive random testing of the whole population, the contact tracing app will largely apply only to those who are symptomatic. We would have to hope that for those without symptoms, R is already quite low – i.e., there may be a possibility of transmission, but at a low frequency.

Secondly, there is the time factor. Once someone develops symptoms, how soon would they become aware of that and report it? One day? Two days? Then the app needs to notify the identified contacts, who are expected to self-isolate. The crucial factor here is whether those contacts will self-isolate quickly enough, before any of them have become infectious. If the original person is infectious for two days before reporting it, and if the identified contacts don’t act quickly, they may well have been infectious themselves for a day or so before they self-isolate.

The third factor is the degree of uptake of the app. The government originally predicted 80% but have backtracked on that to a figure of 50%. Many people regard that as optimistic – some predictions put it as low as 20%. (Bear in mind that only 79% of adults have a smartphone; for those over 65, it is 40%). Concerns over privacy could have a major impact – I can think of several examples of people who wouldn’t want to disclose who they have been in contact with, however much they are told the data is anonymised!

Then we come to the question of numbers. Suppose we have 10,000 cases per day. (Yesterday, 6 May, there were just over 6k positive tests in the UK, from 57,000 people tested, so the actual number of cases is probably much higher than this). And suppose each case had 5 contacts. That makes 50,000 people per day told to self-isolate for a week – giving a total of 350,000 people self-isolating at any one time. The vast majority will not develop symptoms and may regard the exercise as a waste of time. Is this sustainable?

Of course, if distancing works, there shouldn’t be any contacts, but a lot depends on what the app considers as a ‘contact’. How close do you have to be, and for how long?

You may notice that I’ve said very little about testing. Despite all the publicity about the number of tests being done, and how important it is to do much more, it is far from clear how this would contribute towards a contact tracing strategy. If the identified contacts were tested, would this discriminate between those who had been infected and those who hadn’t? If it did, you could release some from isolation. But there is some doubt as to how early in infection the test result becomes positive, and with the current delays in getting the result back to the subject, they would be half-way through their isolation before they were told the result.

Or, if we did random testing of the population, that would identify a lot of people who were infected but asymptomatic. They could be told to self-isolate, and report it to the app, resulting in a large increase in the number of contacts who would in turn need to self-isolate. But if someone who is asymptomatic transmits the disease only occasionally, this does not have much of an effect.

It would be nice if those advocating a large increase in testing would be more explicit about why it is important. I should emphasise that I’m thinking in terms of control strategy in the general population, and not staff and patients in hospitals and care homes, and similar situations, which is a very different matter, and the need for testing there is quite clear.

The final assessment is that potentially it could work, but it will require a very effective publicity campaign, first to convince people to use the app, and then to take notice of the requirement to self-isolate if they have had a reported contact.