Covid-19 Gambles

[Swwils]

If I

Looking back, I didn't really respond to that suggestion.

I'm no virologist or immunologist but, from what little I know about those subjects, my intuitive view would probably be as you suggested - that exposure to an entire pathogen (by their millions/billions) when infected would result in a more robust immune response than does targeting 'just a few little bits' of the pathogen with a vaccine. However, my intuition is presumably wrong, because those who know much more than I do (essentially JCVI) have consistently advised that even those who have had laboratory-confirmed severe Covid-19 infection should nevertheless still be vaccinated.

I see that @Swwils has been around again, so I wonder if he can perhaps shed some light on this?

Kind Regards, John

Yes your institution is likely wrong. The vaccine gives a different, but more robust immune responce compared to a natural infection*. (Generalisation).

High R diseases are always tricky, with measles we have had a highly effective vaccine for decades, really good uptake rates and we still see sporadic outbreaks even in the UK.

Bill gates has had lots of challenges with his foundation and even polio in other countries - public health is very tricky, luckly we have some very smart, dedicated and capable people all around the world.

 

[denso13]

As an aside, I want to dissuade you again from using the term 'deniers'. It is a cheap trope....

It possibly is but I remembered this straight away as I found it somewhat offensive at the time...

I'm asking the lockdown zealots

 

[JohnW2]

Yes your institution is likely wrong....

"Predictive text" usually amuses, but sometimes annoys, me

The vaccine gives a different, but more robust immune responce compared to a natural infection*. (Generalisation).

As I said, I realised from what people had been saying/advising that my intuition was wrong, but it wasn't until you explained some of the issues to me that I understood some of the reasons.

However, I took one of the main points you were making was that a vaccine (certainly an mRNA) one was likely to be more effective against future variants than would infection with the currently prevalent variant - which makes total sense to me. I also understand that if the body's immune system rapidly 'deals with' the virus when one is infected, that might impair the development of (all the components of) a long-lasting immune response. However, that latter point aside, is my intuition perhaps closer to being correct in thinking that the difference between protection provided by infection and vaccine will be less in relation to subsequent encounters with the same variant as caused ones first infection?

I don't think you addressed my other question (in which I personally have somewhat of a vested interest!) about the extent to which your comments (of the superiority of vaccine over infection) apply to 'traditional' vaccines, as well as mRNA ones?

High R diseases are always tricky, with measles we have had a highly effective vaccine for decades, really good uptake rates and we still see sporadic outbreaks even in the UK.

I've always been a bit surprised that it does seem possible to achieve something at least approaching 'herd immunity' with measles (so, again, I assume another flaw in my intuition!). As I understand it, R0 for measles is anything up to 18 ("12-18" is often quoted), which corresponds to a theoretical HIT of around 92% - 94% of the population being totally immune. Given that neither 'vaccine uptake' nor (I presume) 'degree of immunity in the vaccinated' will be "100%", those figures suggest to me that it ought to be a challenge to achieve herd immunity'.

Kind Regards, John

 

[JohnW2]

1) You have assumed that R0 is constant, which it is not, and therefore the rise in case numbers is not exponential (actually it is 'worse' than exponential at first, but becomes 'better' than exponential very quickly and tends toward linear before reaching a peak). The shape of your own graph from March 2020 should tell you that at a glance. ....

R0 doesn't (or shouldn't) change for a particular variant of a particular virus - since it is a measure of transmission of the virus in a totally susceptible (non-immune) population who are 'mixing totally freely', with no restrictions. It is the 'effective' reproduction number (R, Re or Rt) which will change as a result of changes in the susceptible (non-immune) population, formal 'NPIs' or 'informal' changes in behaviour of the population.

Since I have received a couple of questions off-list about this, I thought I would attempt to explain things, as I understand them, in case anyone else is confused and/or interested ...

As above, essentially by definition, R0 (the 'basic reproduction number') for a particular variant of a particulate virus cannot change within a given population (it may differ, but still not ever change, in other countries with different ethnic/whatever characteristics) - since it represents the average number of people who will be infected by one infected person if there is totally free unrestricted mixing within the a totally susceptible population (i.e. no-one with any immunity).

What does change, for various reasons, is the 'effective reproduction number' (R, Re or Rt). This will reduce (to below R0) if any steps are taken to reduce transmission (e.g. formal NPIs, personal behaviour changes etc.) or if the population ceases to be 100% susceptible" (i.e. if some people develop immunity).

There is a lot of talk about 'exponential growth' of the number of new cases although, strictly speaking, this is never possible. Exponential growth implies the same proportionate change over equal time periods (e.g. 50% increase every day, 'doubling every 7 days' etc.) - which would lead in not only the number of new cases increasing every day, but with the rate of rise also increasing every day (since, each day, the rise would be X% of a number greater than the previous day), reflected in the classic shape of an 'exponential curve'.

However, in the context we are discussing, such exponential growth would/could only occur if ('effective') R remained constant (so, exactly the same percentage day-on-day increase every day). However, every time a new patient becomes infected, the proportion of the population who are 'susceptible' decreases slightly (since some are assumed to become immune due to the infection). R will therefore reduce slightly every day, hence the 'rate of rise' (of new cases) will be slightly less that with true 'exponential growth'.

However, having said that, in practical terms that effect is fairly trivial (unless one allows the virus to spread 'totally out of control'). Primarily because they have responded to impending 'waves' by implementing NPIs, no country has had a 'wave' of infection that involved an appreciable proportion of the country's population, so the effect of this progressive decrease in R (hence slowing of 'rate of rise') has, in practice, never been particularly significant.

Even in India, who are just coming out of a wave lasting around 4 months with a peak of just over 4 million reported cases per day (on 1st May), the total number of reported cases between the first day it rose above 40,000 per day (20th March) to the first day it eventually fell back to below 40,000 per day (5th July) was 'only' just over 19 million - a massive number, but only about 1.4% of the country's population, so only resulting in a very small decrease in R (over that entire ~4 month period), hence 'rate of rise' (i.e. deviation from exponential growth). However, small though it is in most countries, this effect is taken into account in many/most of the models used.

That leads to a question. Echoes is correct in saying that, in a good few countries (including the UK), growth of new cases has been far from exponential - although relatively close to exponential at the start of the rise, most of the subsequent rise appears to be closer to linear than exponential (i.e. a much lower, maybe approaching zero, 'rate of increase of the increases' than would occur with exponential growth). So, if, as above, the effect increasing degree of population immunity on R is far too small to account for this, then what is the explanation for this appreciable deviation from exponential growth?

Mathematically, the answer is simple. The only thing that could cause this is a progressive reduction in R for other reasons - but what are those other reasons? No-one knows the answer for certain, but what seems the most credible guess is that when people see (the daily reported numbers of) cases, hospitalisations and deaths rising rapidly, they become increasing compliant with imposed NPIs and, in a good few cases, go beyond the minimum requirements of those NPIs (e.g. keeping 3 or 4 metres away from people, rather than 2 metres, or not meeting people indoors, or going to non-essential shops, even if the 'rules' allow them to). If that's what's been happening, it could explain the progressive reduction in R as the rising phase of a 'wave' worsens - in other words, sensible 'negative feedback' self-imposed by the population.

Contrary to what echoes seems to be suggesting, most modellers do not ignore this and hence just assume 'exponential growth'. Most attempt to include this effect in their models but, of course, they cannot do much more than guess how behaviour will change as people see 'rising numbers' being reported. It's getting a bit easier for them - in that, being now in our third major 'wave' of infection, they can get some handle on that changing behaviour during a 'rising phase' by looking at what happened during the first two waves.

For those who advocate strategies which rely on trying to achieve 'herd immunity' in most (or all) of the population, this is presumably a frustration to them, since human nature being what it is, a substantial proportion of people seeing the numbers 'rise rapidly into the clouds' will probably respond by self-imposing 'protective measures' (even if no mandated ones are in place), thereby potentially greatly extending the period of time required to achieve the desired 'herd immunity' (by infection), even if that is attainable.

I hope that the above makes sense and may be of some help and/or interest to some on my readers (if there are any whio have got this far!).

Kind Regards, John

 

[EFLImpudence]

I can see why they keep getting it wrong.

 

[JohnW2]

I can see why they keep getting it wrong.

I suppose that depends upon which "they" you're talking about. I'm sure it's the case that much of the general public, including much of the media and 'lay' commentators/bloggers whatever do not have a clear understanding of these matters, but I would certainly hope that those who are 'professionally involved' (e.g. epidemiologists, virologists, infectious disease specialists, statisticians, 'modellers', public health folk etc.) would understand far better than I do.

Did what I wrote make any sense to you - and do you think I (attempted to) explain it in a way that might be understandable to at least some?

The latter part of what I wrote was obviously not particularly mathematical but was rather a suggestion that accelerating rises in viral prevalence (i.e. 'exponential growth') are probably at least partially (probably a lot!) being avoided by the public responding sensibly to seeing 'numbers climb', where necessary despite what the government is (or is not) mandating or advising - and maybe our greatest hope for the coming weeks is perhaps that a substantial proportion of the population may continue to be sensible/cautious, maybe even (in the face of what are still 'rapidly rising numbers') in some cases even more cautious than they have been recently - and all that despite government actions!

Kind Regards, John

 

[EFLImpudence]

I will have to study it a bit more.

However, to begin with; something that has puzzled me.

Would I be correct in believing that the Rt number (announced with seeming importance) is a useless statistic because it is only calculated retrospectively, on what has already happened, and is no indication of what might happen next?

 

[Swwils]

It will be hard to compare scenarios, many will say for the short term it does not matter since reinfections on the whole have been milder. It would be different if we had a reinfection or reactivation type issue.

For instance 11 000 healthcare workers who had proved evidence of infection during the first wave of the pandemic in the UK between March and April 2020, none had symptomatic reinfection in the second wave of the virus between October and November 2020. So we are confident natural infection give you robust protection for at least 6 months, likely longer.

PHE indicated natrual infection gives 83% protection against covid-19 reinfections over a five month period.

It's tricky, there are no easy wins.

 

[JohnW2]

I will have to study it a bit more.

Fair enough. If you have questions, or require and clarifications/extensions, just ask.

However, to begin with; something that has puzzled me. ... Would I be correct in believing that the Rt number (announced with seeming importance) is a useless statistic because it is only calculated retrospectively, on what has already happened, and is no indication of what might happen next?

Other than if 'protective measures' change very suddenly and markedly (e.g. the implementation of a 'lockdown' with which most people immediately comply), Rt will only change very slowly and gradually. Hence, whilst what you say is literally true, an Rt 'retrospectively' calculated today (i.e. up to today) will be very close to what it is going to be tomorrow- or indeed, for the next few days or more..

As I said, it's the longer-term changes in Rt (hence longer-term modelling) which are much more difficult to guesstimate (particularly when the population have been told to 'make their own decisions'), since they dependent upon unpredictable (hence not properly modellable) changes in human behaviour in response to the way 'the numbers' are evolving.

Kind Regards, John

 

[EFLImpudence]

A few quick points from a layman:

As above, essentially by definition, R0 (the 'basic reproduction number') for a particular variant of a particulate virus cannot change within a given population (it may differ, but still not ever change,

Ok. I see the difference.

in other countries with different ethnic/whatever characteristics) - since it represents the average number of people who will be infected by one infected person if there is totally free unrestricted mixing within the a totally susceptible population (i.e. no-one with any immunity).

Won't there always be some with natural immunity to cause those 'projections' to be exaggerated?

There is a lot of talk about 'exponential growth' of the number of new cases although, strictly speaking, this is never possible. Exponential growth implies the same proportionate change over equal time periods (e.g. 50% increase every day, 'doubling every 7 days' etc.) - which would lead in not only the number of new cases increasing every day, but with the rate of rise also increasing every day (since, each day, the rise would be X% of a number greater than the previous day), reflected in the classic shape of an 'exponential curve'.

Yet the 'experts' continue to say such things as the current 'doubling every three weeks'.
You, yourself, said cases were doubling every ten days when they were not.

Hypothetical example:
Yesterday there were 10,000 cases; today there were 12,000 new cases.
Rt number is 1.2 - is that correct?
However, a person cannot infect 0.2 of a person, therefore it is not known how many have infected no one else and how many have infected many other people.

I am minded of the situation here at the beginning of the pandemic (if that is what it has been).
In the local borough and surrounding three boroughs, for about, I think it was, three months there were only four (yes four) cases. Then there was an illegal party which led to the 2,000 people there (youngsters obviously) being tested. This led to there now being 1,100 cases in the four boroughs - none of them was ill.
Therefore, for the first ninety days presumably the Rt rate was zero, then on the ninety-first it was presumably 275.
All this time with no idea how many of the population would have tested positive while none was ill.

Even in India, who are just coming out of a wave lasting around 4 months with a peak of just over 4 million reported cases per day (on 1st May), the total number of reported cases between the first day it rose above 40,000 per day (20th March) to the first day it eventually fell back to below 40,000 per day (5th July) was 'only' just over 19 million - a massive number, but only about 1.4% of the country's population, so only resulting in a very small decrease in R (over that entire ~4 month period), hence 'rate of rise' (i.e. deviation from exponential growth). However, small though it is in most countries, this effect is taken into account in many/most of the models used.

Yet the media peddled visions of doom based on the very high numbers without considering the population.
Now India has rates that the UK would be very pleased to have.
Even India's graph is the usual shape.

That leads to a question. Echoes is correct in saying that, in a good few countries (including the UK), growth of new cases has been far from exponential - although relatively close to exponential at the start of the rise, most of the subsequent rise appears to be closer to linear than exponential (i.e. a much lower, maybe approaching zero, 'rate of increase of the increases' than would occur with exponential growth). So, if, as above, the effect increasing degree of population immunity on R is far too small to account for this, then what is the explanation for this appreciable deviation from exponential growth?

Exaggeration and undeniable (stated) fear-mongering at the beginning - maybe justified if claimed for the right reasons but getting tedious.

Are you aware of what is happening in Australia?
Unbelievable restrictions for very few cases (no more than their usual flu rates) and the recent first death this year - a 90+ year old woman. Don't forget it's Winter there.

Mathematically, the answer is simple. The only thing that could cause this is a progressive reduction in R for other reasons - but what are those other reasons? No-one knows the answer for certain, but what seems the most credible guess is that when people see (the daily reported numbers of) cases, hospitalisations and deaths rising rapidly, they become increasing compliant with imposed NPIs and, in a good few cases, go beyond the minimum requirements of those NPIs (e.g. keeping 3 or 4 metres away from people, rather than 2 metres, or not meeting people indoors, or going to non-essential shops, even if the 'rules' allow them to). If that's what's been happening, it could explain the progressive reduction in R as the rising phase of a 'wave' worsens - in other words, sensible 'negative feedback' self-imposed by the population.

Or - that's just what happens. A lot of the graphs seem to be the same shape despite what the countries have done.
How many people are naturally immune - for whatever reasons?

Contrary to what echoes seems to be suggesting, most modellers do not ignore this and hence just assume 'exponential growth'. Most attempt to include this effect in their models but, of course, they cannot do much more than guess how behaviour will change as people see 'rising numbers' being reported. It's getting a bit easier for them - in that, being now in our third major 'wave' of infection, they can get some handle on that changing behaviour during a 'rising phase' by looking at what happened during the first two waves.

Do you mean looking at what they previously got wrong?

For those who advocate strategies which rely on trying to achieve 'herd immunity' in most (or all) of the population, this is presumably a frustration to them, since human nature being what it is, a substantial proportion of people seeing the numbers 'rise rapidly into the clouds' will probably respond by self-imposing 'protective measures' (even if no mandated ones are in place), thereby potentially greatly extending the period of time required to achieve the desired 'herd immunity' (by infection), even if that is attainable.

Are we classed as having herd immunity against flu and the common cold?
If not then I would suppose it cannot be achieved.

 

[Notch7]

Are we classed as having herd immunity against flu and the common cold?
If not then I would suppose it cannot be achieved

flu vaccine is not effective against different strains.

common cold is a symptom not a disease, it has 200 or so causes.

 

[EFLImpudence]

Is that a 'no'?

 

[JohnW2]

For instance 11 000 healthcare workers who had proved evidence of infection during the first wave of the pandemic in the UK between March and April 2020, none had symptomatic reinfection in the second wave of the virus between October and November 2020.

Very interesting. Is there any similar data for the main part of what most people regard as the 'second wave' (although I agree that one might argue that is was 'the third', given what happened prior to November, and was 'curtailed' by the November lockdown)?

I ask because those people would have been infected (during the first wave) by the 'original virus', and I imagine that, during much of October/November, the dominant variant was still that 'original' virus, whereas from December onwards the alpha variant became progressively more dominant - and you previously suggested (as seems very reasonable) that natural infection would probably offer less (if any!) protection against future variants than would an mRNA be likely to do.

So we are confident natural infection give you robust protection for at least 6 months, likely longer. ... PHE indicated natrual infection gives 83% protection against covid-19 reinfections over a five month period.

As above, do we know whether that "robust protection for at least 6 months" and the "83% protection over 5 months" relate only to protection against the variant with which they were initially infected, or also to protection against subsequently-appearing variants?

If the latter, then that would presumably considerably limit the scope for (as you suggested) an mRNA vaccine to be more likely to protect against 'future variants' than does natural infection?

Kind Regards, John

 

[JohnW2]

Won't there always be some with natural immunity to cause those 'projections' to be exaggerated?

Thanks for having taken the time to study and critique/question all of which I wrote. In view of the length of your comments, I'm going to split my response into a number of bite-sized (by my standards!) posts.

As for the above, there will always be ('natural'/'intrinsic') variations in 'individual susceptibility' to any infectious disease (even if no-one has ever previously been exposed to the pathogen concerned), and that is what R0 is really reflecting. Given a particular degree of contact/proximity with others, a person infected with the original Covid virus (R ~3) would (in a 'non-immune' population) have infected, on average, about 3 people, whereas, with the same degree of contact/proximity, a person infected with measles (R0 up to 18) may (again in a 'non-immune' population) would infect, on average, up to 18 others.

I suppose that one way of looking at it is that R0 is the average degree of ('intrinsic' - not due to infection of vaccine) susceptibility/'immunity' to a particular infection.

Yet the 'experts' continue to say such things as the current 'doubling every three weeks'.

I agree that some do, even though they should (and do) 'know better' - except, of course, if/when it is true.

You, yourself, said cases were doubling every ten days when they were not.

If I said that, I shouldn't have done so when it wasn't true - I should have talked about "it being said that" cases were doubling every 10 days.

Hypothetical example: Yesterday there were 10,000 cases; today there were 12,000 new cases. Rt number is 1.2 - is that correct?

No - and, unfortunately, you're forcing me to deal with more technicalities. In common with many, you are confusing R0 with Growth Rate. Rt indicates the total number of people who will be infected by one infected person, but that will happen over a period of several days, not all on one day. There is a lot written about the relationship between Rt and Growth Rate (and indices of the period over which transmission occurs), both on the govt website and elsewhere.

In the very roughest of terms, since transmission from one infected person occurs, on average, over a period of about 5 days, the daily Growth Rate will be roughly one-fifth of Rt. Hence you will see govt figures such as this recent one below - where, as you can see, a daily growth rate of 4% corresponds to an Rt of 1.20 (i.e. "20%" increase). Therefore, using your figures, a daily increase (growth rate) of 20% would correspond to an Rt of roughly 2.0 ("a "100%" increase)

However, a person cannot infect 0.2 of a person, therefore it is not known how many have infected no one else and how many have infected many other people.

Well, for a start, as above, your Rt was not Rt, but was a Growth Rate. However, in terms of Rt, it's obviously just a matter of how we present the figures. If Rt were 1.2, interpreted as "each infected person infects, on average, 1.2 others", you complain that one "cannot infect 0.2 of a person" - but if you interpreted it as meaning "100 infected people infect, on average, 120 others", you presumably would have no reason for complaint. Don't forget that we are, necessarily, always talking about 'on average'.

I am minded of the situation here at the beginning of the pandemic (if that is what it has been). In the local borough and surrounding three boroughs, for about, I think it was, three months there were only four (yes four) cases. Then there was an illegal party which led to the 2,000 people there (youngsters obviously) being tested. This led to there now being 1,100 cases in the four boroughs - none of them was ill. Therefore, for the first ninety days presumably the Rt rate was zero, then on the ninety-first it was presumably 275.
All this time with no idea how many of the population would have tested positive while none was ill.

It is obviously ridiculous to think about, or talk about, Rt when a massive rise in transmission is due to a single, and very brief event.

I do, however, rather struggle to understand the figures you are quoting. Are you really suggesting (by implication/assumption) that over 50% of those attending a party were infected, and also that all 1,100 infected people were asymptomatic "non of them was ill")?

Yet the media peddled visions of doom based on the very high numbers without considering the population.

I cannot speak for, or defend, their stupidity. Having said that, if 1,100 infected/infectious people (particularly if they were all asymptomatic) suddenly appeared in a population that had previously only seen four cases in three months, then there could well be serious concern about how that was going to 'pan out' as things moved forward.

... enough for this first post, I reckon ... more to come.

Kind Regards, John

 

[EFLImpudence]

I do, however, rather struggle to understand the figures you are quoting. Are you really suggesting (by implication/assumption) that over 50% of those attending a party were infected, and also that all 1,100 infected people were asymptomatic "non of them was ill")?

Well, that is how it was reported - correct or not.

90 days 4 cases; next day party and 1,100 cases.


On my hypothetical numbers; would it have been correct if five days apart (instead of yesterday and today)?

When I said that a person cannot infect 0.2 of another person, obviously I realise that it refers to a percentage and 100 infecting 120 is possible but it is no indication of the actual numbers - it cannot be evenly spread.

Whether 80 infected another 80 and 20 infected 40 - or any other combination - is not known unless there were a party, for example.