Coronavirus - Modelling Aspects Only

[XFool]

Interesting general article about COVID-19 and modelling!

How modelling Covid has changed the way we think about epidemics
Adam Kucharski

The Guardian

The pandemic has created a tragic ‘natural experiment’ - a once-in-a-century jolt that could produce unexpected insights

"Adam Kucharski is an associate professor at the London School of Hygiene & Tropical Medicine and author of The Rules of Contagion"


Includes this interesting link, which may already be known to posters on here: https://covidsim.org/v3.20201206/?place=gb

[johnhemming]

My current plan is to do a least squares fit to the first differential of the Gompertz curve for the seasonal wave by trust when I get this week's data.

That will give some form of numerical forecast as to when hospital admissions will peak.

I have found an interesting paper on this
https://www.sciencedirect.com/science/a ... 2704000032

However, I think I will probably give a range of reasonable assumptions to the code rather than do something purely abstract.

Does anyone have any suggestions about this?

[zico]

Seems clear now that it'll be a race between the new virus spreading and the vaccination, so I've tried a bit of simple modelling on this.
I've used the IFR's by age from the following paper.

https://www.imperial.ac.uk/media/imperi ... ort-34.pdf

Plugging the IFR's into England & Wales census data gives an IFR of .86% for the UK. (Imperial's figure is actually 1.15% for a country such as ours).
Based on these IFRs, I've estimated the IFRs for the UK vaccination group priority list.
I also assumed 2 million vacs per week and 80% protection after first dose.

My starting point is to make a worst case estimate of what would happen if the 70% more infectious new virus spread so quickly that everyone was infected.
That worst case scenario is 550,000 deaths - though it's assuming NHS isn't overwhelmed, so true worst case scenario could easily be double or treble that (but hopefully that's too apocalyptic to actually happen).

The good news bit is that if the most vulnerable are vaccinated at the rate of 2m per week, then in 7 weeks, 75% of the potential deaths will have been averted (assuming 80% protection from 1st jab - there are various estimates around of this protection - Pfizer said 52%, Van Tam says 89% so a HUGE difference there).
To vaccinate all the most vulnerable groups (all the way down to 50-54 year olds) would take 19 weeks (1st jab only).

There's a big problem here however, which is that today's govt plan is to give the 2nd jab 12 weeks later. At 2m jabs per week, that would mean 60-64 year olds (and younger) wouldn't get their first jab until the higher priority groups had received their 2nd jab, so not until 25 weeks later which equates to late-June before 60-64 start to gain any vaccine protection (A pain for anyone in the 60-64 bracket, but deaths in this age group would only account for 10% of all deaths, but that's still potentially 70,000 deaths in the 50-64 age group, if all were infected).

[dealtn]

Seems clear now that it'll be a race between the new virus spreading and the vaccination, so I've tried a bit of simple modelling on this.
I've used the IFR's by age from the following paper.

https://www.imperial.ac.uk/media/imperi ... ort-34.pdf

Plugging the IFR's into England & Wales census data gives an IFR of .86% for the UK. (Imperial's figure is actually 1.15% for a country such as ours).
Based on these IFRs, I've estimated the IFRs for the UK vaccination group priority list.
I also assumed 2 million vacs per week and 80% protection after first dose.

My starting point is to make a worst case estimate of what would happen if the 70% more infectious new virus spread so quickly that everyone was infected.
That worst case scenario is 550,000 deaths - though it's assuming NHS isn't overwhelmed, so true worst case scenario could easily be double or treble that (but hopefully that's too apocalyptic to actually happen).

The good news bit is that if the most vulnerable are vaccinated at the rate of 2m per week, then in 7 weeks, 75% of the potential deaths will have been averted (assuming 80% protection from 1st jab - there are various estimates around of this protection - Pfizer said 52%, Van Tam says 89% so a HUGE difference there).
To vaccinate all the most vulnerable groups (all the way down to 50-54 year olds) would take 19 weeks (1st jab only).

There's a big problem here however, which is that today's govt plan is to give the 2nd jab 12 weeks later. At 2m jabs per week, that would mean 60-64 year olds (and younger) wouldn't get their first jab until the higher priority groups had received their 2nd jab, so not until 25 weeks later which equates to late-June before 60-64 start to gain any vaccine protection (A pain for anyone in the 60-64 bracket, but deaths in this age group would only account for 10% of all deaths, but that's still potentially 70,000 deaths in the 50-64 age group, if all were infected).

The vaccination not only reduces your chance of catching it, but also what the implication might be if you do catch it, doesn't it?

That's a 2 factor effect. On the ability to catch it, and the IFR if you do. Or am I wrong?

[johnhemming]

Seems clear now that it'll be a race between the new virus spreading and the vaccination, so I've tried a bit of simple modelling on this.
I've used the IFR's by age from the following paper.

The problem is that the IFR varies by the season. We are now in the bad season. That does not mean 0.86% is too low, but it is a relevant issue.

Additionally there never was 100% susceptibility.

[zico]

The vaccination not only reduces your chance of catching it, but also what the implication might be if you do catch it, doesn't it?

That's a 2 factor effect. On the ability to catch it, and the IFR if you do. Or am I wrong?

I've assumes 80% reduction on chance of fatality. Just an estimate, because there's still a huge gap between Van Tam and Pfizer's estimate.

[servodude]

Seems clear now that it'll be a race between the new virus spreading and the vaccination, so I've tried a bit of simple modelling on this.
I've used the IFR's by age from the following paper.

The problem is that the IFR varies by the season. We are now in the bad season. That does not mean 0.86% is too low, but it is a relevant issue.

Additionally there never was 100% susceptibility.

I've not seen anything to indicate the IFR for COVID changes by any noticeable measure seasonally (it's a novel virus after all)
- even though as expected the rate of infection has

I'm guessing you're assuming that the main seasonal factor is viral load? rather than exposure
- both will increase during "winter" as people spend more time together indoors, windows shut, etc
- if it helps... you can consider not being exposed to an infected person as keeping the viral load to 0: this should be your target
- there probably will be work done eventually which manages to establish the optimal amount of virus to encounter (i.e. enough to work as an inoculum - so it stresses the immune system enough to remember it, but with no risk of disease) but I've not seen it yet unfortunately

If you look at the IFR of COVID vs age: https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v7.full-text
- and the demographic of the UK: https://www.statista.com/statistics/281174/uk-population-by-age/
- for a uniform infection spread you'd be looking at an IFR of about 1.1%

The difficulty will be stopping that spread from being concentrated in places where there are the most at risk living together indoors
- you won't notice this thing circulating in schools (because kids get colds all the time - they're indoors together a lot in winter after all)
- but you will notice if it gets in to aged care homes as lots of old people will die in quick succession

- sd

EDIT: it's always the tags

[dealtn]

The vaccination not only reduces your chance of catching it, but also what the implication might be if you do catch it, doesn't it?

That's a 2 factor effect. On the ability to catch it, and the IFR if you do. Or am I wrong?

I've assumes 80% reduction on chance of fatality. Just an estimate, because there's still a huge gap between Van Tam and Pfizer's estimate.

I'm still not clear, apologies.

You originally claimed a 80% protection. So is that 80% less chance of catching it or 80% less chance of dying from it? Where are you getting that 80% from?

So you have a population size, and a start proportion of those that have it. Then you have a rate those who have it, spread it, and that is deemed constant? Presumably this spreading can only be done to people that haven't already had it, so a shrinking pool? Presumably you are assuming 100% susceptibility too? No allowance made for people that, for whatever (non-vaccine) reason can't get it?

Then you are vaccinating the population in order of the (descending) highest IFR, with a single jab, at a constant rate? Have you made any assumptions about whether these vaccinated individuals can infect others, and at what different rate to an unvaccinated individual?

The you are applying an efficacy rate on the vaccinated individuals to calculate whether they can get it? Then are you applying an IFR that is the same IFR as an unvaccinated person in that risk group, or a different one?

I know you claimed it to be a simple model, but I don't think simplicity works. It will be an interesting model to develop though. Any other variables that should be considered?

[servodude]

So you have a population size, and a start proportion of those that have it. Then you have a rate those who have it, spread it, and that is deemed constant? Presumably this spreading can only be done to people that haven't already had it, so a shrinking pool? Presumably you are assuming 100% susceptibility too? No allowance made for people that, for whatever (non-vaccine) reason can't get it?

The numbers in the UK are still in the fuzzy edges of what could go wrong

Official death tally is ~75k
Number of people in census over 90 is 0.6million

from https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v7.full-text the IFR exceeds 25% for ages 90 and above
so for the kind of "back of a fag packet what if everyone gets it" scenario being touted to compare the impact of the variants (i.e. start with drawing your asymptotes) the effect of what the virus has already done on the numbers is pretty minimal
- or would be accounted for by half of the people in the UK over 90 having had it

- sd

[servodude]

Plugging the IFR's into England & Wales census data gives an IFR of .86% for the UK. (Imperial's figure is actually 1.15% for a country such as ours).

I get much closer to the Imperial figure convolving the graphs I've seen
- was your 0.86 based on using the value for the lower age over the histogram ranges?

- sd

[dealtn]

So you have a population size, and a start proportion of those that have it. Then you have a rate those who have it, spread it, and that is deemed constant? Presumably this spreading can only be done to people that haven't already had it, so a shrinking pool? Presumably you are assuming 100% susceptibility too? No allowance made for people that, for whatever (non-vaccine) reason can't get it?

The numbers in the UK are still in the fuzzy edges of what could go wrong

Official death tally is ~75k
Number of people in census over 90 is 0.6million

from https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v7.full-text the IFR exceeds 25% for ages 90 and above
so for the kind of "back of a fag packet what if everyone gets it" scenario being touted to compare the impact of the variants (i.e. start with drawing your asymptotes) the effect of what the virus has already done on the numbers is pretty minimal
- or would be accounted for by half of the people in the UK over 90 having had it

- sd

Apologies (again!) I don't understand what you are saying, or criticising, in my trying to establish the starting conditions for the model that is proposed.

[servodude]

So you have a population size, and a start proportion of those that have it. Then you have a rate those who have it, spread it, and that is deemed constant? Presumably this spreading can only be done to people that haven't already had it, so a shrinking pool? Presumably you are assuming 100% susceptibility too? No allowance made for people that, for whatever (non-vaccine) reason can't get it?

The numbers in the UK are still in the fuzzy edges of what could go wrong

Official death tally is ~75k
Number of people in census over 90 is 0.6million

from https://www.medrxiv.org/content/10.1101/2020.07.23.20160895v7.full-text the IFR exceeds 25% for ages 90 and above
so for the kind of "back of a fag packet what if everyone gets it" scenario being touted to compare the impact of the variants (i.e. start with drawing your asymptotes) the effect of what the virus has already done on the numbers is pretty minimal
- or would be accounted for by half of the people in the UK over 90 having had it

- sd

Apologies (again!) I don't understand what you are saying, or criticising, in my trying to establish the starting conditions for the model that is proposed.

That's OK - don't worry there's no criticism meant

If you consider the "variant" as a change to the system of the virus in the population what Zico was describing was similar to plotting the asymptotes
- for each option: what happens at "infinity" what happens at zero (gives a "response" more than a "model" really)

that can help compare the differences between them and initial conditions are normally irrelevant, or identical for the two posited case

- sd

[zico]

The vaccination not only reduces your chance of catching it, but also what the implication might be if you do catch it, doesn't it?

That's a 2 factor effect. On the ability to catch it, and the IFR if you do. Or am I wrong?

I've assumes 80% reduction on chance of fatality. Just an estimate, because there's still a huge gap between Van Tam and Pfizer's estimate.

I'm still not clear, apologies.

You originally claimed a 80% protection. So is that 80% less chance of catching it or 80% less chance of dying from it? Where are you getting that 80% from?

So you have a population size, and a start proportion of those that have it. Then you have a rate those who have it, spread it, and that is deemed constant? Presumably this spreading can only be done to people that haven't already had it, so a shrinking pool? Presumably you are assuming 100% susceptibility too? No allowance made for people that, for whatever (non-vaccine) reason can't get it?

Then you are vaccinating the population in order of the (descending) highest IFR, with a single jab, at a constant rate? Have you made any assumptions about whether these vaccinated individuals can infect others, and at what different rate to an unvaccinated individual?

The you are applying an efficacy rate on the vaccinated individuals to calculate whether they can get it? Then are you applying an IFR that is the same IFR as an unvaccinated person in that risk group, or a different one?

I know you claimed it to be a simple model, but I don't think simplicity works. It will be an interesting model to develop though. Any other variables that should be considered?

I'm using 80% as the reduction in chance of dying from it. So for a particular cohort, if pre-vac IFR = 10%, then post-vac IFR = 2%.
(80% is an approximation of the effect of just 1 jab vaccination, a guesstimate because Pfizer say 52% and Van Tam says 89%)

I've made a simple assumption that everyone in the country gets infected (obviously too simple, but at least it's clear what I'm doing). If you think 50% (say) of people would get infected, then you simply divide all my numbers by 2.

The main thing I was trying to get a handle on is what percentage of potential deaths will be stopped by the vaccination programme, so I found it a useful exercise. Quite understand if others don't find it useful.

My assumptions on IFR's (and number unvaccinated deaths in brackets - assuming 100% of the group are infected)
16% IFR (64,000 deaths ) Care Home Residents (assuming they have same rate as 90+ year olds)
0.1% IFR (1,000 d) Care Home Workers (assuming they're evenly distributed between 20-60 years old)
2% (68,000 d) 80+ year olds (assuming 80+ year old in bad health are in the Care Homes group)
0.1% (2,000 d) Health and Social Care Workers (same assumption as for Care Home Workers)
3% (69,000 d) 75-79 year olds
2% IFR (66,000 d) 70-74 year olds
7% (154,000 d ) Extremely vulnerable (just a guess really - used around 50% of Care Home Residents)
1% (34,000 d ) 65-69 year olds
1% (43,000 d) 16-64 year olds with health conditions (just a guess, assumed they'd be like healthy 65-69 year olds)
0.9% (34,000 deaths) 60-64 year olds
0.6% (26,000) 55-59 year olds
0.4% IFR (19,000 deaths) 50-54 year olds
The tricky bits are estimating/guessing how the Extremely Vulnerable and Existing Health Conditions groups affect the more general age groups.

After watching PM briefing tonight, I was struck by him saying the most vulnerable groups could receive a vaccination by mid-Feb. There are 14 million in the groups he mentioned, so they'd need to do 2.5 million jabs per week (even higher than the 2 million that's being touted around).

[servodude]

I was struck by him saying the most vulnerable groups could receive a vaccination by mid-Feb.

"Most vulnerable" will mean what it needs to for this to be true (enough) - you just have to start at the right end of the spread and work the other way

-sd

[johnhemming]

I've not seen anything to indicate the IFR for COVID changes by any noticeable measure seasonally (it's a novel virus after all)

Places like Maneus look to have had a really high IFR, Similarly the European winter bout looks to be quite heavy. It fits with the viral load being heavier.

I am not aware of any papers on this, but it appears to be where the outcomes point when you look at how bad things have been recently in Germany compared to Gangelt's 0.24% from about April last year. (not sure of precise dating).

[johnhemming]

I thought I would get some figures from Sweden now it appears their second wave is close to ending.

I think the answers are approx 560 deaths per million population in the first wave and
300 deaths per million population in the second wave.

It is worth seeing how this compares to other countries. My impression from the figures is that the bigger the first wave the smaller the second, but actually the second wave reduced by more than the increase in the first wave. However, I have not gone through all the countries doing the calculation I have relied on the fact that Swedens position in on Worldometers is going down the chart.

[dealtn]

I'm using 80% as the reduction in chance of dying from it. So for a particular cohort, if pre-vac IFR = 10%, then post-vac IFR = 2%.
(80% is an approximation of the effect of just 1 jab vaccination, a guesstimate because Pfizer say 52% and Van Tam says 89%)

I've made a simple assumption that everyone in the country gets infected (obviously too simple, but at least it's clear what I'm doing). If you think 50% (say) of people would get infected, then you simply divide all my numbers by 2.

The main thing I was trying to get a handle on is what percentage of potential deaths will be stopped by the vaccination programme, so I found it a useful exercise. Quite understand if others don't find it useful.

(I have only selectively quoted for purposes of brevity)

Where are the 52% and 89% from? As far as I am aware they are "efficacy" rates, and specifically efficacy from a single jab, not the normal double dose. The efficacy rate is not the same thing as a reduction in the IFR.

My understanding is the efficacy is a measure in how much prevention you have "getting" the infection. In addition to that there is the consideration that IF you get it, what then is the result. The IFR is specifically fatality rate of someone infected is it not?

If you look at the results of the Oxford/AZN vaccination trials for instance not only were the trial sample prevented from getting it (up to about 90% on some measures, but 55% perhaps on a single dose), but of those that did nobody died. Now the sample size of infected people is too small (a triumph of the vaccine combined with few people > 60 years old) but that might be relevant too.

On your second point you don't simply divide by 2, that is a huge error!

If your start point is 100% susceptibility that's fine, but can be argued against. If it's 50% then the pool of potential people still to be infected is reduced by more than 50%. The possibilities, and pace of infection drop considerably. That's how herd immunity begins to work (be that through getting it, vaccination, or behaviour change). The reduction in pace has a huge impact on the end numbers of deaths, as the vaccination programme (which carries on at the same pace) massively outpaces the infection spread.

Consider 2 start positions for where we are now.

Position A. Everyone can (and will if left untreated) get it, and so far only 10% of the population have had it. To get to here approx. 75k have died.

Position B. Only 75% of the population are susceptible, and so far 20% of the population have had it.

With say 50 million in the population, Position A has 45 million still susceptible. Position B has 27.5 million.

If we also assume that once anyone has got it (and recovered or died) they both can't pass it on or get it again (you can argue these assumptions too) then the difference is huge.

Now if the chances of spreading it rely on an uninfected person being exposed to an infected one, the differences in how many can potentially get it, and then become potential spreaders themselves, which determine how fast the pandemic spreads, relative to the opposite effect from the vaccination programme, have huge implications in the model for the predicted fatalities from this point.

[servodude]

I've not seen anything to indicate the IFR for COVID changes by any noticeable measure seasonally (it's a novel virus after all)

Places like Maneus look to have had a really high IFR, Similarly the European winter bout looks to be quite heavy. It fits with the viral load being heavier.

I am not aware of any papers on this, but it appears to be where the outcomes point when you look at how bad things have been recently in Germany compared to Gangelt's 0.24% from about April last year. (not sure of precise dating).

It fits with a lot of things
- I'm disinclined to single out any particular one to the exclusion of others
examples might be:
- there are more other infections around in winter
- vitamin D naturally lower
- more sedentary indoor behaviour
- travel for seasonal festivals

And I don't think the weather in Manaus varies much over the year (mid 20s to 30s?)

- sd

[johnhemming]

It fits with a lot of things

I am sure someone will do the work properly some time.

[servodude]

It fits with a lot of things

I am sure someone will do the work properly some time.

Yeah you're probably right