Coronavirus - Modelling Aspects Only

[Nimrod103]

It has now been reported (https://www.telegraph.co.uk/news/2020/0 ... t-new-low/) that hospital deaths have dropped below the long term average. It is interesting to ponder what the total 2020 deaths will be compared to previous years, if Covid has just accelerated the demise of the elderly by a few months.

[johnhemming]

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

Neither median nor mean are dependent on the units you pick.

[GoSeigen]

\
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

I was the poster who initially queried johnhemming. I think it's clear now that he was merely expressing an opinion about lockdown not affecting peak infections. He offered no evidence in the form of studies, professional opinion or a coherently argued case to demonstrate its truth. [Not unusual for a politician...]

I've no problem with posters offering an opinion, and don't really care too much whether it's right or wrong. My own view is that far too little is still understood about the virus and epidemic to make unqualified assertions of the sort JH made; I have very little confidence in my own understanding of the epidemic, which FWIW, I believe still has to run the majority of its course.

As for lockdown affecting peak deaths, I really see little difference between the UK timing and Wuhan's: does JH believe that the Wuhan lockdown also was too late to affect its peak death rate? How does he know? Does he have an example of a place where the lockdown was effective? How about South Africa, for example, which instituted a very early, very strict lockdown?


GS

[johnhemming]

I was the poster who initially queried johnhemming. I think it's clear now that he was merely expressing an opinion about lockdown not affecting peak infections. He offered no evidence in the form of studies, professional opinion or a coherently argued case to demonstrate its truth. [Not unusual for a politician...]

That, of course, is your opinion.

[servodude]

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

Neither median nor mean are dependent on the units you pick.

Yes and that is convenient for the maths
But inconveniently neither gives you the necessary value for extrapolating backwards
-sd

[johnhemming]

But inconveniently neither gives you the necessary value for extrapolating backwards

Where is the evidence for that (in writing rather than an audio or video recording)?

[johnhemming]

This came in on another thread
https://www.cell.com/action/showPdf?pii ... %2930610-3

However, it is the same info as from Singapore, but instead from the USA.

Importantly, we detected SARS-CoV-2-reactive CD4+ T cells in
40%–60% of unexposed individuals, suggesting crossreactive T cell recognition between circulating ‘‘common cold’’ coronaviruses and SARS-CoV-2.

Apart from the significance for modelling it also gives the cox pox type solution to Covid-19 vaccination in that people can get infected by another coronavirus and get some protection.

[zico]

It has now been reported (https://www.telegraph.co.uk/news/2020/0 ... t-new-low/) that hospital deaths have dropped below the long term average. It is interesting to ponder what the total 2020 deaths will be compared to previous years, if Covid has just accelerated the demise of the elderly by a few months.

Studies have shown that people dying of Covid would on average have more than 10 more years to live if not for the virus. Here's a link to one.

https://www.businessinsider.com/study-f ... ?r=US&IR=T

[Nimrod103]

It has now been reported (https://www.telegraph.co.uk/news/2020/0 ... t-new-low/) that hospital deaths have dropped below the long term average. It is interesting to ponder what the total 2020 deaths will be compared to previous years, if Covid has just accelerated the demise of the elderly by a few months.

Studies have shown that people dying of Covid would on average have more than 10 more years to live if not for the virus. Here's a link to one.

https://www.businessinsider.com/study-f ... ?r=US&IR=T

A study, not studies. This Italian example I find hard to believe. In the UK we know about a third of deaths have been in care homes, and the average stay in a care home before death, as I recall is 2-3 years. And the vast majority of deaths have been to the over 70s, and with significant life limiting medical conditions.

[zico]

A quote from the Glasgow study of Italian deaths.
"Among people dying of COVID-19, the number of years of life lost per person appear similar to diseases such as coronary heart disease,"

Here's one using Florida data that gives 12.5 years per person.

https://statmodeling.stat.columbia.edu/ ... ronavirus/

It seems intuitively unlikely that people aged 70+ have quite a few more years left to live, but that's why there are studies to estimate this sort of thing.

Here's an interesting Swiss study on the opposite situation, health effects of lockdown "This loss would be entirely borne by 2.1% of the population, who will suffer an average 9.79 YLL".

https://www.medrxiv.org/content/10.1101 ... 20069716v3

[swill453]

It seems intuitively unlikely that people aged 70+ have quite a few more years left to live, but that's why there are studies to estimate this sort of thing.

I know the Covid-19 death rate is higher for those with underlying health conditions, but the average life expectancy for a 70 year old male is that they would live another 16 years (18 years for a female).

Even an 85 year old male would be expected to live 6 more years on average.

https://www.ons.gov.uk/peoplepopulation ... 2019-06-07

Scott.

[servodude]

But inconveniently neither gives you the necessary value for extrapolating backwards

Where is the evidence for that (in writing rather than an audio or video recording)?

see the example in the data set i posted in the earlier thread
- or have a listen to the podcast mentioned - it's not long
- or consider something like this for a pdf; it's not even that skewed

- skew it more and see the mode move early

there was a book we used to use by Scharf - there might be more up to date texts

you seem to be acting as though the choice does make a difference - i don't have the data set so I can't say

- sd

[servodude]

But inconveniently neither gives you the necessary value for extrapolating backwards

Where is the evidence for that (in writing rather than an audio or video recording)?

see the example in the data set i posted in the earlier thread
- or have a listen to the podcast mentioned - it's not long
- or consider something like this for a pdf; it's not even that skewed

ah perhaps it's not obvious to all what this implies
OK lets take the Feynman 'if you can't explain it to a 7 year old" approach - i.e. if it's not clear after this post it's my fault!

we're assuming a spread of times from infection to death - imagine it looks like that arbitrary graph in my previous post
for the purposes of which average to choose the shape doesn't matter it's just a distribution: that has a mean, median and mode

now consider a single day of infection
- imagine there was one day only when everyone in a population was infected
- where does the peak for that day occur? at the mean, median or mode?

i think for that case its clear that it's the mode ? (that's basically its definition)

so now consider a series of days where an increasing population are being infected every day
- and then that stops, after the day of most infections no more people are infected
for every successive day there is a peak at the mode of the time to death distribution
- but it is over-layed and obscured/dwarfed by that of the day following
until the absolute peak falls at the mode of the distribution function after the day of maximum infection (because no-one is infected later)

and then it gets a bit noisy in real life because:
- there isn't a day where infections absolutely stop (unless you got the lockdown right and we know they didn't)
- the distribution function is not accurately known (it's being inferred from empirical measurements )
- and the increases day on day are not smooth

but it still holds that the day of maximum death follows the day of maximum infection by the mode of the distribution function for infection to time of death

calculating the function for the spread of time to death is difficult
- the shape of that function will determine how wrong the median and mean are for the purposes of extrapolating back

i hope that's helped
- sd

[9873210]

so now consider a series of days where an increasing population are being infected every day
- and then that stops, after the day of most infections no more people are infected
for every successive day there is a peak at the mode of the time to death distribution
- but it is over-layed and obscured/dwarfed by that of the day following
until the absolute peak falls at the mode of the distribution function after the day of maximum infection (because no-one is infected later)

The bold is not necessarily true. I can't explain it a 7-year old because they don't understand counterexamples, but the following shows that the claim is not true.
Consider the case where

1% die 1 day after infection
2% die 2 days after infection
3% die 3 days after infection
4% die 4 days after infection
And the rest recover,
The mode for deaths is 4 days after infection.


Now let the number of infections be
99, 100, 101, 102, 103, 000, 000, 0000, 000, 0, 0
deaths will be
xx, xxx, xxx, xxx, 10, 10.1, 9.16, 7.17, 4.12, 0, 0
(The xxx are because those calculation requires infection data from days that are not given, long zeros are for alignment)

The peak deaths occur on the day after peak infections, not four days after peak infections.

The delay between peak infections and peak deaths depends on both the shape of the peak in infections and the shape of the peak in the mortality curve. For a lot of reasonable cases the delay will be the mode, but "reasonable cases" makes assumptions about the shapes of the peaks.

but it still holds that the day of maximum death follows the day of maximum infection by the mode of the distribution function for infection to time of death

As above it does not hold.

[servodude]

so now consider a series of days where an increasing population are being infected every day
- and then that stops, after the day of most infections no more people are infected
for every successive day there is a peak at the mode of the time to death distribution
- but it is over-layed and obscured/dwarfed by that of the day following
until the absolute peak falls at the mode of the distribution function after the day of maximum infection (because no-one is infected later)

The bold is not necessarily true. I can't explain it a 7-year old because they don't understand counterexamples, but the following shows that the claim is not true.
Consider the case where

1% die 1 day after infection
2% die 2 days after infection
3% die 3 days after infection
4% die 4 days after infection
And the rest recover,
The mode for deaths is 4 days after infection.


Now let the number of infections be
99, 100, 101, 102, 103, 000, 000, 0000, 000, 0, 0
deaths will be
xx, xxx, xxx, xxx, 10, 10.1, 9.16, 7.17, 4.12, 0, 0
(The xxx are because those calculation requires infection data from days that are not given, long zeros are for alignment)

The peak deaths occur on the day after peak infections, not four days after peak infections.

The delay between peak infections and peak deaths depends on both the shape of the peak in infections and the shape of the peak in the mortality curve. For a lot of reasonable cases the delay will be the mode, but "reasonable cases" makes assumptions about the shapes of the peaks.

but it still holds that the day of maximum death follows the day of maximum infection by the mode of the distribution function for infection to time of death

As above it does not hold.

True
I had approached the superposition part from with the assumptions that:
- the distribution was weighted towards the early
- and growth was sufficient to dwarf previous days

Apologies & thanks
- sd

[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....

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.

Thanks. I struggle to grasp even the most basic of statistics sometimes.

So the 278k is the cumulative total number of confirmed cases in the UK so far? If yes, this 278k figure strikes me as no help at all for the purpose of the conversation at the time, which was how close we are to achieving herd immunity IIRC. I think the 278k figure only includes people ill enough to have presented at hospital and tested positive.

The important number when considering herd immunity or not, is how many have actually been infected, and the 278k figure is probably dwarfed by the number of people who have been infected asymptomatically, plus those who have been infected symptomatically but not badly enough to end up in hospital or get tested. These two figures are completely unknown, and are the reason I questioned your 1 in 200. I don't think we have any idea of the true situation.

The nearest we get is the study of the small town of Vo in Italy where everyone in the town was tested, and 30% IIRC turned out to be positive. Other studies have come up with results in the range of 4% to 80% AIUI, so no help at all there!

[johnhemming]

i hope that's helped
- sd

I think the difficulty with this is that there are considerable uncertainties. We don't know the numbers of infections each day before the peak date of infection, we don't know the number of infections after the peak date of infection. We don't actually know the peak date of infection. Many infections are within households and one would assume that superspreader events had been stopped substantially before lockdown. Hence it is entirely possible that the peak rate of infection occurred slightly after lockdown. [because of greater exposure, but I don't think this is the case]

We don't actually have a distribution function for deaths following infection. We don't know if there is an early peak of deaths from people who were already at death's door and then a later, but lower peak of deaths with an inevitably long tail. Hence we don't really know.

What we know is that the peak rate of hospital deaths in England was on 8th April. We know that lockdown came in on 23rd March. The basic question is one as to whether or not there was enough time between lockdown and the peak rate of hospital deaths for one to have caused the other.

On the information I have there isn't. On the information I have it appears that the peak rate of infection was prior to lockdown.

[dspp]

i hope that's helped
- sd

I think the difficulty with this is that there are considerable uncertainties. We don't know the numbers of infections each day before the peak date of infection, we don't know the number of infections after the peak date of infection. We don't actually know the peak date of infection. Many infections are within households and one would assume that superspreader events had been stopped substantially before lockdown. Hence it is entirely possible that the peak rate of infection occurred slightly after lockdown. [because of greater exposure, but I don't think this is the case]

We don't actually have a distribution function for deaths following infection. We don't know if there is an early peak of deaths from people who were already at death's door and then a later, but lower peak of deaths with an inevitably long tail. Hence we don't really know.

What we know is that the peak rate of hospital deaths in England was on 8th April. We know that lockdown came in on 23rd March. The basic question is one as to whether or not there was enough time between lockdown and the peak rate of hospital deaths for one to have caused the other.

On the information I have there isn't. On the information I have it appears that the peak rate of infection was prior to lockdown.

Official gov lockdown was 23 March. Citizen led lockdown started earlier. So not a classic step function, more of a fast ramp.

Agree with everything else.

regards, dspp

[zico]

I've done some more longer-term modelling for a couple of scenarios (graphs below) using as a starting point the government estimate of 8,000 current daily infections, ONS deaths figures to mid-May of 40,000 plus SAGE's IFR estimate of 0.63% and various R-values.
For both scenarios I've assumed R=1.1 until 4th July, then R=1.2 after further planned easing of lockdown measures, and R=1 after Feb 28th 2021.

Scenario A - R=1.2 for July & August, R=0.8 (lockdown) in Sep, Oct & Nov R=1.2, Dec R=0.8, Jan/Feb R=1.2
Scenario B - R=1.2 for July/Aug/Sep, then R=0.8 (lockdown) Oct & Nov, R=1.2 Dec, Jan lockdown, Feb, R=1.2

A few points jump out immediately.
1. If a vaccine isn't available until end-2021, herd immunity is unavoidable. Also applies if a vaccine can never be found.
2. With either of these scenarios, we'll need to spend one-third of the time in lockdown until a vaccine is available.
3. After easing lockdown, if we delay going back into lockdown by one month, we'll need to spend the same overall time in lockdown anyway, but will have an extra 20,000 deaths (based on R=1.2 assumption).

Obviously, you can use different assumptions, but it seems unrealistic to assume UK can get economy anywhere near fully functioning while still keep R-values below 1.2 or similar levels.

Date of vaccine availability is obviously the key variable here for the total number of UK deaths.

Seems to me to be very likely that government will ease lockdown until end-October, as that scenario keeps daily deaths under 600/day, which is something that NHS can cope with.

[9873210]

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.

Thanks. I struggle to grasp even the most basic of statistics sometimes.

So the 278k is the cumulative total number of confirmed cases in the UK so far? If yes, this 278k figure strikes me as no help at all for the purpose of the conversation at the time, which was how close we are to achieving herd immunity IIRC. I think the 278k figure only includes people ill enough to have presented at hospital and tested positive.

The important number when considering herd immunity or not, is how many have actually been infected, and the 278k figure is probably dwarfed by the number of people who have been infected asymptomatically, plus those who have been infected symptomatically but not badly enough to end up in hospital or get tested. These two figures are completely unknown, and are the reason I questioned your 1 in 200. I don't think we have any idea of the true situation.

The nearest we get is the study of the small town of Vo in Italy where everyone in the town was tested, and 30% IIRC turned out to be positive. Other studies have come up with results in the range of 4% to 80% AIUI, so no help at all there!

I'm not addressing herd immunity here, I'm addressing whether the generic you personally knows somebody who is known to be infected. The latter is important because it affects how people will respond, and how best to communicate with them. These will in turn affect how the epidemic plays out.