Coronavirus - Modelling Aspects Only

[Mike4]

Sub-herd immunity seems like pretty sound logic to me, but very difficult to measure.
I've also been scratching my head about London's much sharper decline in cases than any other region. Here's my hypothesis for people to shoot at (unsupported by data).

What's different about London? Public transport (especially tube) probably used far more intensively than any other city in UK. So, lots of packed tubes/trains/buses for fairly long commutes in very close proximity to lots of different people (particularly tubes). If you assume each tube journey is a potential "superspreader" event, then if most people stop using public transport, then the potential for infection falls dramatically.

Ok, my totally unsupported-by-data reading of this would be that the speculation that people who have previously caught corona virus colds have some sort of pre-loaded immunity to COVID-19, might turn out to be true.

Now due to the concentration of London population in tube trains etc Londoners are more likely to have has a corona type of cold in the past. So if true, the London population was already half way to herd immunity while the lab technicians in China were still designing SARS-CoV-2, let alone carelessly letting it escape. (Am I allowed to say that last bit?)

[johnhemming]

Remembering that an unknown proportion of people have been identified to be at least partially immune to Covid-19 based probably on previous Coronavirus infections and there may be others that are not susceptible for other reasons it is most like that London and possibly a substantial part of the South East have hit the infection level at which herd partial immunity reduces infection rates. I think that is also likely for the bigger cities.

[zico]

Interesting ONS update for w/e 22nd May (Week 21)

England and Wales figures only. Week 21 excess deaths now 2,348 (+26%) more than 5-year average. Still on a downward trend, but not back to normal yet. (Total excess deaths since start of Covid-19 are now 56,308)

https://www.ons.gov.uk/peoplepopulation ... g22may2020

In light of our London discussion, there's some interesting new figures on the excess deaths percentage by region for week 21 only.
I'd expected London to have the lowest percentage, but Wales & South-West are much lower.
(Maybe this is surprising because London had the highest peak (+300%) so looking at the graphs, it looks to have got back to almost-normal)
However, deaths lag infections by quite a bit, so this isn't inconsistent with London having a sharper fall in infection rates.

North East 40.8%
East 30.3%
Yorkshire 28.8%
West Midlands 27.9%
South East 25.2%
London 23.6%
East Midlands 23.5%
North West 22.3%
Wales 12.7%
South West 8.1%

[servodude]

Total excess deaths since start of Covid-19 are now 56,308

Is there still much of an attempt to blame anything other than miss counting for these being so much more than the "official" figure?

-sd

[zico]

Total excess deaths since start of Covid-19 are now 56,308

Is there still much of an attempt to blame anything other than miss counting for these being so much more than the "official" figure?

-sd

I think it's fair enough for the Government to publish the various definitions of deaths, as long as they set the definitions out clearly, and explain them well. The ONS (Office for National Statistics) is a gold standard in this regard.

We have at least 3 definitions, all of which are reasonable.
- Deaths from people who tested positive for Covid-19.
- The above, plus cases where there was no positive test, but doctors consider the symptoms to be consistent with Covid-19
- Excess deaths, accepted by the UK government amongst others as the "best" measure. This is a good measure because it doesn't rely on individual diagnoses, and is particularly useful in cases such as this pandemic, where there is a clear event and a large difference between the normal 5-year average figures. It also takes into account other deaths indirectly caused by the pandemic, such as fewer road traffic deaths, delayed life-saving operations, deaths because people didn't go to hospital when it was an emergency etc.

Yesterday, a daily increase of 111 was announced. This is a reasonable and correct statement.
However, the overall deaths figure increased by 556 because analysts had found 445 people who hadn't previously been counted as having had a positive Covid-19 test because the test was done by private labs, but they are now included in the figures. A pity this wasn't explained at the daily briefing.

[zico]

New government study examining effects of various factors. I've just skimmed it and picked out a couple of interesting (to me anyway) quotes.

https://assets.publishing.service.gov.u ... review.pdf

A survival analysis looked at people with a positive test, and those 80 or older, when compared with those under 40, were seventy times more likely to die. These are the largest disparities found in this analysis. Working age males diagnosed with COVID-19 were twice as likely to die as females.The majority of excess deaths (75%) occurred in those aged 75 and over. COVID-19 deaths were equivalent to 80% of the excess in every age group, except the oldest age group where this proportion is lower. There have been fewer deaths than expected in children under 15 years of age.

This increase in mortality by age is also observed among hospitalised patients; data from the same study of 16,649 COVID-19 positive patients showed that, even after adjusting for comorbidities, sex and obesity, the risk of dying among those over 80 was almost 14 times higher than those under 50 years old

[tjh290633]

I would still, however, expect some deaths in a second wave later this year in London and the South East.

I'm not sure that we ever had a first wave in our part of the South East. I don't know of anyone who has had it, anyone who has died of it, or anyone hospitalised because of it.

What few cases there seem to have been are probably imported from London, and the first recorded case in the country was down here, but didn't seem to lead to a major outbreak.

TJH

[redsturgeon]

I know of one person who had it, never met them, they are a work colleague of my wife. They caught it from their daughter (a nurse) and their husband also had it, none required hospital treatment.

John

[9873210]

Sub-herd immunity seems like pretty sound logic to me, but very difficult to measure.

Six degrees of Kevin Bacon.

Sub-herds are unlikely to exist in any meaningful way. Human interactions are typically a scale free network. The connectivity of the network affects the speed of spread, but it has already done so. The historical spread rate already takes this into account. Any social distancing measures will reduce the number of connections but unless they are very specifically and aggressively targeted (e.g. a ring of armed guards on the M25, or New Zealand banning travel) they are unlikely to change the scale free nature of the network.

To put it another way everybody is a member of dozens of sub-herds and there is enough overlap that there are very few, if any, firebreaks.

A really efficient contact trace and quarantine system could be viewed as a way to cutout a sub-herd of the infected, but I don't think that's the best way to view contact tracing.

Changing the subject slightly. If we had a limit number of vaccines for greatest results we should immunize the most highly connected people. This is pretty much the opposite of immunizing a sub-herd.

[9873210]

The known infection rate is about one in two hundred. Do you know the status of two hundred people?

[Itsallaguess]

Sub-herds are unlikely to exist in any meaningful way.

Human interactions are typically a scale free network. The connectivity of the network affects the speed of spread, but it has already done so. The historical spread rate already takes this into account. Any social distancing measures will reduce the number of connections but unless they are very specifically and aggressively targeted (e.g. a ring of armed guards on the M25, or New Zealand banning travel) they are unlikely to change the scale free nature of the network.

To put it another way everybody is a member of dozens of sub-herds and there is enough overlap that there are very few, if any, firebreaks.

Didn't the lock-downs severely reduce the number of normally-accessed sub-herds for most people though?

I know mine have severely reduced over the last few months, and I would say this is true of almost everyone I know as well..

Cheers,

Itsallaguess

[Mike4]

The known infection rate is about one in two hundred. Do you know the status of two hundred people?

Eh????? Where are you getting that from please? A link or a reference of some sort would be appreciated.

I'm not even sure what you mean by "infection rate". R0 is believed to be a shade below 1.0 at the moment, which means each infected person infects slightly fewer than one other person. Could you expand on what "one in two hundred" actually means please?

Thanks....

[servodude]

The known infection rate is about one in two hundred. Do you know the status of two hundred people?

Eh????? Where are you getting that from please? A link or a reference of some sort would be appreciated.

I'm not even sure what you mean by "infection rate". R0 is believed to be a shade below 1.0 at the moment, which means each infected person infects slightly fewer than one other person. Could you expand on what "one in two hundred" actually means please?

Thanks....

It looks to be the ballpark IFR (0.5) that's been bandied about
- i guess the point might be if 1 in 200 succumb you'd likely need to know about 200 people before you personally known one (if everyone had it)

- sd

[9873210]

The known infection rate is about one in two hundred. Do you know the status of two hundred people?

Eh????? Where are you getting that from please? A link or a reference of some sort would be appreciated.

I'm not even sure what you mean by "infection rate". R0 is believed to be a shade below 1.0 at the moment, which means each infected person infects slightly fewer than one other person. Could you expand on what "one in two hundred" actually means please?

Thanks....

https://www.google.com/search?q=coronavirus+cases+in+the+UK

This shows there are 278k confirmed cases in the UK. Divide that by the population of the UK (About 66 million) and round to get that 1/200 people in the UK are known to have been infected. Other web sites will give broadly similar values.

If you learn the status of 200 randomly selected people you will, on average, know about 1 confirmed case.

I know the status of fewer than a couple of dozen (non-randomly selected) personal contacts. So it is not surprising that I know of no personal contact who has a confirmed case. (Baring celebrities such as John Conway).

Many people can claim to know thousands of people, but that does not mean they know the status of thousands of people. I, like many other people, value my privacy and very few of the people who know me know whether or not I have been infected. It is not surprising that many people do not know anybody who is known to have been infected.

[servodude]

I have posted about this before. The steps are .
a) Someone gets infected
b) They show symptoms
c) If Ill enough they get admitted to hospital
d) They may go into ICU
e) they may get ventilated
f) They die (if ill enough)

The government have access to reliable figures for c, d, e and f.

The evidence is that a-f is at least on median average 23 days. In fact probably longer.

Hence if the peak of deaths in England was on 8th April then you can work backwards to the date of peak infection.

I'm not saying you're wrong, but there's a couple of things that are raising alarm bells.
Hopefully you might find time to consider them.

How does this model cope with the fact we suspect the deaths in hospital to be only 60% of the story: do we just assume that the pattern for deaths outside are the same? that people are not more likely to live longer if receiving treatment?

Another is in the use of median time between infection and death. As linked to earlier in the "BBC more or less podcast Kit Yates" (of https://www.amazon.co.uk/Maths-Life-Dea ... 1787475425) uses the mode.
Which to me makes more sense
- it's the peak of the probability density function
- it's the "most likely" time after infection that someone will die

Consider a very skewed distribution by way of example
- lets have a minimum number of days N that it takes for someone to die
- and say 25% succumb on the first day, 10% on the second, 5% on the third day then 2% every day after
So everyone that's going to die has died in a about month
For that distribution the mode is N, the median is N+8 the average is N+12(approx)
Seems pretty clear that the mode is the value to use if you're extrapolating backwards
- obviously it might not make a difference depending on the distribution of values
- but where it does then I think it's the more correct value to use - why choose median over it?

We would expect the time do death to be skewed towards the earlier limit: given frailty of the elderly, people with DNR directives
- i actually expect it to look a bit like a long bath tub as mechanical assistance gets turned off at the other end

As I said I'm not saying your wrong but I don't think it's possibly to say categorically with the data we have that the behavioural changes caused by lockdown had no effect on the peak.

- sd

[9873210]

Didn't the lock-downs severely reduce the number of normally-accessed sub-herds for most people though?

I know mine have severely reduced over the last few months, and I would say this is true of almost everyone I know as well..

Cheers,

Itsallaguess

[In the following I use island as a synonym for sub-herd. It's the terminology I'm use to and it looked wrong when I tried s/island/sub-herd/g.]

We may each have reduced our contacts from hundreds or thousands to single digits. But an average of single digit contacts per person is plenty to maintain a richly connected network without substantial isolated islands.

In a scale free network when you start randomly removing links you eventually get more and more tiny islands (mostly one node, some with two, a few larger) while the rest of the network hangs together right up to the end. You do not get many mid sized islands. You have a main network which is gradually getting smaller and less redundant, and scattered isolated individuals that are totally out of the game.

I'd expect there to be some households that really good at social distancing and truly isolated, but the rest of us are connected to one or more postman, grocer, nurse, etc. I'd expect almost all of those essential workers to be well enough connected that we are all connected to each other. Perhaps with 12 degrees of separation rather than 6.

Notice I'm not saying social distances doesn't work, I'm just saying it's unlikely to create islands that you have to consider separately.

[servodude]

I'd expect there to be some households that really good at social distancing and truly isolated, but the rest of us are connected to one or more postman, grocer, nurse, etc. I'd expect almost all of those essential workers to be well enough connected that we are all connected to each other. Perhaps with 12 degrees of separation rather than 6.

I would certainly agree with this as to how the exposure of individuals/groups works
- transmission though requires a certain level of exposure/degree of interaction

- there is a group of people to whom I am more likely to pass this (or contract it from) because of the nature of my relationships with them

- sd

[johnhemming]

How does this model cope with the fact we suspect the deaths in hospital to be only 60% of the story: do we just assume that the pattern for deaths outside are the same? that people are not more likely to live longer if receiving treatment?

Another is in the use of median time between infection and death. As linked to earlier in the "BBC more or less podcast Kit Yates" (of https://www.amazon.co.uk/Maths-Life-Dea ... 1787475425) uses the mode.

We have to work from the best information that we have. We do have figures for the dates of deaths in hospitals. That enables working out the peak date of infection for those people. People in care homes are most likely to have been infected by someone in the care home. Hence that does not really demonstrate the wider societal pattern of infection, it more demonstrates how bad we have been a protecting people in care homes.

I am quite uncomfortable myself using a "mode" because it very much depends upon the units that you pick.

[spasmodicus]

New government study examining effects of various factors. I've just skimmed it and picked out a couple of interesting (to me anyway) quotes.

https://assets.publishing.service.gov.u ... review.pdf

A survival analysis looked at people with a positive test, and those 80 or older, when compared with those under 40, were seventy times more likely to die. These are the largest disparities found in this analysis. Working age males diagnosed with COVID-19 were twice as likely to die as females.The majority of excess deaths (75%) occurred in those aged 75 and over. COVID-19 deaths were equivalent to 80% of the excess in every age group, except the oldest age group where this proportion is lower. There have been fewer deaths than expected in children under 15 years of age.

This increase in mortality by age is also observed among hospitalised patients; data from the same study of 16,649 COVID-19 positive patients showed that, even after adjusting for comorbidities, sex and obesity, the risk of dying among those over 80 was almost 14 times higher than those under 50 years old

That sounds dramatic, but the increase in mortality by age to some extent reflects the non-COVID19 mortality by age.
http://www.bandolier.org.uk/booth/Risk/dyingage.html
suggests that risk of death over 1 year (men)
age 45-54 one in 279
age 75-84 one in 15
a ratio of 18.6:1
of course, the figures should be integrated (see graph in url) to get a better comparison with over 80 vs under 80. It would come out at a lot more than 18.6:1. This suggests that if your are over 80, your risk of dying from other causes over the year is much greater than your risk of dying from covid19, even assuming that you become infected with it.

S

[servodude]

We have to work from the best information that we have. We do have figures for the dates of deaths in hospitals. That enables working out the peak date of infection for those people. People in care homes are most likely to have been infected by someone in the care home. Hence that does not really demonstrate the wider societal pattern of infection, it more demonstrates how bad we have been a protecting people in care homes.

I'm pretty used to having to account for noise in systems when modelling/simulating them
- there's a lot of noise in the observable facts around this and it appears to not be accounted for in most of the coverage
That sets alarms off when there are claims made that don't account for or even acknowledge this
I expect that from the govt (as I don't trust them with figures on this) but this seems to be a good forum for thinking out loud about these kind of things more objectively

I am quite uncomfortable myself using a "mode" because it very much depends upon the units that you pick.

a lot can also depend on which average you pick to extrapolate back
If the mode is hard to establish accurately that does not mean that using the median is equivalent
if the choice makes a difference and you choose one because of convenience or comfort it leaves the conclusions open to a bit of suspicion
- or at least I'd treat any claims based on them as being less than categorical


anyway the mode is just a lazy empirical shortcut for "most likely value" (the old "E" expected value in stochastics)
in my head it should be possible to synthesise from the data a smooth probability density function (best fit over the convolution of the data for a month?) the for the time to death that gives a truer most likely value
- the mode would probably work for this if you have enough sample points (and they're accurate etc etc)
- but I don't think we do

it's very much one of those "all models are wrong but" some are wrong in different ways scenarios

- sd