Coronavirus - Modelling Aspects Only

[Nimrod103]

I have found the graphs and charts issued by COBR useful over the last few weeks, but I have only located them on the Daily Mail website, which has not carried them for the last two days, Does anyone know where they can be found online?

This may help you, it is the link I get in the .gov email each day, slides as pdf and dataset as .xls

https://www.gov.uk/government/publicati ... tent=daily

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

for some reason they seem to have gorn from todays. That makes me smell a rat.

regards, dspp

It would appear my nose for detecting rats is on target, and there is something whiffy in No10,

https://www.theguardian.com/world/live/ ... -continues - see 14:35

"No 10 fails to commit to resuming publication of global deaths comparison chart in daily slides
Andrew Sparrow Andrew Sparrow
The Downing Street lobby briefing has just finished. Here are the main points.

The prime minister’s spokesman refused to confirm that the government remained committed to publishing its usual daily slides, including the global deaths comparison chart. The government did publish slides yesterday, but not the usual ones including a slide showing a global deaths and another showing transport use. The spokesman said he could not say whether these slides would be used again. The government would be showing slides about the roadmap to recovery, he said. The transport use slide was moderately awkward for the government because last week it showed a small but steady increase in people travelling at a time when that was not being encouraged. Here is the one from Saturday last week.
..
But ministers were particularly embarrassed by the global deaths comparison chart. Even though it compares countries that compile their figures in different ways, and it gives total deaths not deaths per head, it looked damning because it showed the UK as having the worst death rate in Europe - and, as the days went on, this became more prominent. Here is the chart from Saturday.
.."

- dspp

The Govt were publishing comparisons while they were using Spieghalter's Guardian article defence that death measurements in different countries were not comparable. AIUI, he specifically told the Govt not to use his explanation, probably because he has a political axe to grind, so the Govt might say - why publish the data then.

[genou]

The Govt were publishing comparisons while they were using Spieghalter's Guardian article defence that death measurements in different countries were not comparable. AIUI, he specifically told the Govt not to use his explanation, probably because he has a political axe to grind, so the Govt might say - why publish the data then.

You can see him give his reasons here - https://parliamentlive.tv/event/index/b ... n=15:39:26

[dspp]

This may help you, it is the link I get in the .gov email each day, slides as pdf and dataset as .xls

https://www.gov.uk/government/publicati ... tent=daily

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

for some reason they seem to have gorn from todays. That makes me smell a rat.

regards, dspp

It would appear my nose for detecting rats is on target, and there is something whiffy in No10,

https://www.theguardian.com/world/live/ ... -continues - see 14:35

"No 10 fails to commit to resuming publication of global deaths comparison chart in daily slides
Andrew Sparrow Andrew Sparrow
The Downing Street lobby briefing has just finished. Here are the main points.

The prime minister’s spokesman refused to confirm that the government remained committed to publishing its usual daily slides, including the global deaths comparison chart. The government did publish slides yesterday, but not the usual ones including a slide showing a global deaths and another showing transport use. The spokesman said he could not say whether these slides would be used again. The government would be showing slides about the roadmap to recovery, he said. The transport use slide was moderately awkward for the government because last week it showed a small but steady increase in people travelling at a time when that was not being encouraged. Here is the one from Saturday last week.
..
But ministers were particularly embarrassed by the global deaths comparison chart. Even though it compares countries that compile their figures in different ways, and it gives total deaths not deaths per head, it looked damning because it showed the UK as having the worst death rate in Europe - and, as the days went on, this became more prominent. Here is the chart from Saturday.
.."

- dspp

The Govt were publishing comparisons while they were using Spieghalter's Guardian article defence that death measurements in different countries were not comparable. AIUI, he specifically told the Govt not to use his explanation, probably because he has a political axe to grind, so the Govt might say - why publish the data then.

For the same reasons as I have stated, plus the reasons that pertained from the get-go: to watch the trends.

regards, dspp

[Sorcery]

This paper says 58% needed for herd immunity, compared to 70% that Vallance said. Certainly lower, but not that different.

Figures 4 and 5 are the key ones ion the article.

From the conclusion :
<i>In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5. If it were around 17%, which evidence from Stockholm County suggests the resulting fatalities from infections prior to the HIT being reached should be a very low proportion of the population.<i>

Thanks for the correction - I'd only skimmed it very quickly so missed that the first graph referred to homogenous populations.

I've read it a bit more carefully now, and although it's too dense for me to fully understand it, I have 3 major objections.

1. "Sense test 1". UK scientific advice has been that benefits from herd immunity are only achieved at 60%+ levels. If the author (Nic Lewis) is correct, than most UK scientists are wrong. Possible, but unlikely, unless he's a world-renowned scientist with a track record of being correct with his minority views. So, how good are the author's scientific credentials and is he recognised as a leading scientist? Which brings us to point 2.

2. "Sense test 2". From Wikipedia.

Nic Lewis. A semiretired successful financier from Bath, England, with a strong mathematics and physics background, Mr. Lewis has made significant contributions to the subject of climate change

So he is not a scientist. He is however a climate change denier, which puts him at odds with over 99% of actual scientists. Again, maybe he's right and virtually all scientists are wrong, but doesn't seem too likely.

3. In his quote below, he makes the big assumption that because the new cases had stopped increasing by 11th April, HIT (Herd Immunity Threshold) had been reached. But surely new cases could stop increasing for a variety of other (and more likely) reasons? Greater public awareness, practising social distancing, hand-washing, fewer people out and about.

Very sensibly, the Swedish public health authority has surveyed the prevalence of antibodies to the SARS-COV-2 virus in Stockholm County, the earliest in Sweden hit by COVID-19. They thereby estimated that 17% of the population would have been infected by 11 April, rising to 25% by 1 May 2020.[5] Yet recorded new cases had stopped increasing by 11 April (Figure 1), as had net hospital admissions,[6] and both measures have fallen significantly since. That pattern indicates that the HIT had been reached by 11April, at which point only 17% of the population appear to have been infected.

Ok perhaps with better spelling and formatting this time.

Re Sense test 1. As I understand it the herd immunity level is a function of Rate of infection, except nobody knows R until the pandemic has passed. It's a derived number from a formula. He defines it in his replies to comments as the point at which new infections = closed (dead or recovered) cases (on any given day presumably).
Nic Lewis I find to be very polite. He is also very able numerically, as you might expect with a mathematics and a physics background, his education from his website is not displayed, a plus for modesty then. How can you say he is not a scientist? Have seen him in "bulletin board" real time critique a professional scientific paper on it's math shortcomings and get an almost instant admission by the paper author of it's problems.

Re Sense test 2.
Then off you go categorising people as climate change deniers. That would be impolite and incorrect. Nobody denies ice ages.

No point going any further really.

[Sorcery]

Didn't mean to stop the discussion if that's what happened.

Going back to the Nic Lewis paper, someone else commented they had very similar thought. Followed his link and came up with this :
https://jsmp.dk/posts/2020-05-07-herdimmunity/
The section on Heterogeneous infectiousness is the most relevant. Heterogeneous is the opposite of Homogeneous if that helps.

Another day though, so more information has arrived, this one via email https://arxiv.org/pdf/2005.03085.pdf

Different and more pessimistic but very relevant and working on different aspects of heterogenity. They say :
The current model took age cohorts and social activity levels into account. However,
more complex and realistic models have many other types of heterogeneities: for instance
increased spreading within households (of different sizes) or within schools and workplaces;
and spatial aspects with rural areas having lower contact rates than metropolitan regions.
It seems reasonable to assume that most such additional heterogeneities will have the effect
of lowering the disease-induced immunity level hDS even further, in that high spreading
environments (metropolitan regions, large households, big workplaces, ...) will have a
higher fraction infected thus resulting in immunity being concentrated even more on highly
active individuals

That sounds very close to confirmation of Nic Lewis's post.

I have replied to Nic's post on the original link to it,

Stephen Anthony | May 13, 2020 at 7:42 am | Reply
Nic,

I am seriously impressed by your work here. I have not replicated a heterogenous model such as yours, which is what I would need to do to be absolutely sure.
It explains why the peak infected totals of the Diamond Princess, Theodore Roosevellt aircraft carrier and the Italian town of Vo are so low.
The classical idea that infected population increases until the HIT is equal to 1 – (1/Ro) as a proportion is now defunct.
I would never have guessed that a heterogenous model could bring the HIT so far down. In my head I had been playing around with ideas like proportions of the popuiation as “Uninfectable”, “Resistant” and perhaps exercised immune systems as offering some explanation of what we have seen in the example locations mentioned above.

What role do you see for changed behaviour in response to the virus if any?
or
Would a heterogenous rat population produce the same results?

Regards, Steve

No reply yet, I imagine he is getting a lot of feedback. It does sound as if the HIT (Herd Immunity Thresh-hold) = to 1 – (1/Ro), is a dead parrot as the saying goes.
This looks as if it's becoming a paradigm shift in epidemiology.
Good news for all of us if true.

[zico]

This was published yesterday by one of the bodies that feeds into the SAGE to calculate the R number that tops the agenda at their bi-weekly meeting.
Well worth a click because it's quite readable stuff, and on the "Key Values" bit, you can select various measures. What they call the "Attack Rate" is the % of the population that has been infected. The estimate is 12% (which seems much higher than what Vallance said yesterday).

I'm not quite sure what the database is, but from the explanation, it sounds like it might be based on all hospital cases??

England's IFR (Infection Fatality Rate is estimated as 0.63% (conf int 0.49%-0.81%)

A lot of the estimates are surprisingly precise. For example, East of England R-value = 0.71 (confidence interval 0.68-0.74).

https://joshuablake.github.io/public-RTM-reports/

Some really interesting (and encouraging) stuff here. Graph on infections and deaths show infections falling like a stone in recent days. (This is likely to be much more accurate than government's "daily new infections" chart, because testing has increased 4-fold or more during the life of the daily "new infections" chart.)
However - big caveat - recent death numbers appear to be falling a lot more slowly than the estimate in these curves - which only use actuals up to 5th May.

London's "Attack Rate" is 20% so if Nic Lewis's paper is correct, London already has herd immunity and today's pictures of crowds of people on buses and tubes with no social distancing may be nothing to worry about, but clearly Government is being a lot more cautious.

[zico]

Good blog from David Spiegelhalter. He's talking in this about the population fatality rate (as opposed to the infection fatality rate) and basically making the point about this being far higher risks for older people.

https://medium.com/wintoncentre/what-ar ... 28695aea69

[zico]

Didn't mean to stop the discussion if that's what happened.

Going back to the Nic Lewis paper, someone else commented they had very similar thought. Followed his link and came up with this :
https://jsmp.dk/posts/2020-05-07-herdimmunity/
The section on Heterogeneous infectiousness is the most relevant. Heterogeneous is the opposite of Homogeneous if that helps.

Another day though, so more information has arrived, this one via email https://arxiv.org/pdf/2005.03085.pdf

Different and more pessimistic but very relevant and working on different aspects of heterogenity. They say :
The current model took age cohorts and social activity levels into account. However,
more complex and realistic models have many other types of heterogeneities: for instance
increased spreading within households (of different sizes) or within schools and workplaces;
and spatial aspects with rural areas having lower contact rates than metropolitan regions.
It seems reasonable to assume that most such additional heterogeneities will have the effect
of lowering the disease-induced immunity level hDS even further, in that high spreading
environments (metropolitan regions, large households, big workplaces, ...) will have a
higher fraction infected thus resulting in immunity being concentrated even more on highly
active individuals

That sounds very close to confirmation of Nic Lewis's post.

I have replied to Nic's post on the original link to it,

Stephen Anthony | May 13, 2020 at 7:42 am | Reply
Nic,

I am seriously impressed by your work here. I have not replicated a heterogenous model such as yours, which is what I would need to do to be absolutely sure.
It explains why the peak infected totals of the Diamond Princess, Theodore Roosevellt aircraft carrier and the Italian town of Vo are so low.
The classical idea that infected population increases until the HIT is equal to 1 – (1/Ro) as a proportion is now defunct.
I would never have guessed that a heterogenous model could bring the HIT so far down. In my head I had been playing around with ideas like proportions of the popuiation as “Uninfectable”, “Resistant” and perhaps exercised immune systems as offering some explanation of what we have seen in the example locations mentioned above.

What role do you see for changed behaviour in response to the virus if any?
or
Would a heterogenous rat population produce the same results?

Regards, Steve

No reply yet, I imagine he is getting a lot of feedback. It does sound as if the HIT (Herd Immunity Thresh-hold) = to 1 – (1/Ro), is a dead parrot as the saying goes.
This looks as if it's becoming a paradigm shift in epidemiology.
Good news for all of us if true.

Thanks for the extra links. My initial reaction is that there is probably something in this, but herd immunity of 7% just looked way too implausible. Just thinking about it at the personal level, I'm hoping my personal probability of being infected would be far less than 70% (even if that was the population of UK citizens infected) because I'm being far more careful than most people, and I wouldn't be at all surprised if there's a significant cohort of people like me in the population. Let's call them Careful Active Rational Pensioners (because I like acronyms!). There are probably similar sub-groups (Risk Averse Mothers) and their kids (RAMlets). Interested in this paragraph below from one of your links, which seems to indicate that if a virus spreads so quickly that people aren't aware and don't have chance to modify their behaviour, then the Herd Immunity rate would be higher.

Some people argue that the threshold cannot be less than in the 60s, since some Italian cities have at least that level. However, we can see here that it depends on the momentum. The above simulations end up at about 40%, whereas a simulation with the same parameters but higher momentum ends up at 70% infected.

[stockton]

For those interested, the preliminary results of a population wide antibody test in Spain indicate that about 5% of the population have Coronavirus antibodies.

[Itsallaguess]

Not sure if this has been posted already, but I've just noticed that the 'Worldometers' site is now showing 'Outcome of cases' data for Italy and Spain, which show interesting and encouraging improvements over time in the Covid recovery-rates in both countries -



Sources for both of the above images -

Italy - https://www.worldometers.info/coronavirus/country/italy/

Spain - https://www.worldometers.info/coronavirus/country/spain/

Given that we're still at a relatively early stage of investigation into this virus, there's a chance that things might get more encouraging still, given the above steady improvements...

Cheers,

Itsallaguess

[zico]

Seems to me these kinds of graphs would inevitably show this pattern over time. People die quickly, but take months to recover. Maybe I'm missing something?

[johnhemming]

For those interested, the preliminary results of a population wide antibody test in Spain indicate that about 5% of the population have Coronavirus antibodies.

I would be particularly interested by such an analysis by age cohorts. My hypothesis is that younger people beat off the virus by using T cells and prior to generating antibodies, but older people need the antibody response. Hence you would expect a higher proportion of the older cohorts to have antibodies.

[stockton]

I would be particularly interested by such an analysis by age cohorts. My hypothesis is that younger people beat off the virus by using T cells and prior to generating antibodies, but older people need the antibody response. Hence you would expect a higher proportion of the older cohorts to have antibodies.

https://www.mscbs.gob.es/gabinetePrensa ... 528614.pdf
There is a table by age on page 8.

[johnhemming]

Thanks for that. It does seem that the antibody is more prevalent in older cohorts.

[spasmodicus]

I said a few days ago

meanwhile, on 14th May the ONS will be publishing the first regular update on its random testing

https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurvey/england10may2020#covid-19-infection-survey

preliminary results are stated for swab tests conducted in England between 26 April and 8 May 2020

https://www.ons.gov.uk/peoplepopulation ... d14may2020


Moderator Note : I've edited this to link to the ONS pilot referred to, and to remove the non-modelling bit related to government policy - that's better suited to Polite Discussions board. Keen to keep this board free for purely modelling and data discussions.

[modellingman]

Not sure if this has been posted already, but I've just noticed that the 'Worldometers' site is now showing 'Outcome of cases' data for Italy and Spain, which show interesting and encouraging improvements over time in the Covid recovery-rates in both countries -



Sources for both of the above images -

Italy - https://www.worldometers.info/coronavirus/country/italy/

Spain - https://www.worldometers.info/coronavirus/country/spain/

Given that we're still at a relatively early stage of investigation into this virus, there's a chance that things might get more encouraging still, given the above steady improvements...

Cheers,

Itsallaguess

I think Zico is right.

The graphs simply show deaths and recovereds as a proportion of deaths+recovereds (and this also explains why they are symmetrical about the 50% horizontal line). They are also based, in the main, on hospitalised cases where, I suspect, the average time to death is less than the average time to recovery. If my suspicion is correct, then in any daily cohort of cases the measured fatality rate will be biassed towards overestimation until sufficient time has elapsed to know the outcome of all cases in that cohort, though the degree of bias decreases with time.

The fatality rate at a point in time as shown in Worldometer's graphs is simply derived from the measured fatality rates at that point in time of all the daily cohorts prior to that point (in fact it is a weighted sum of the measured rates where the weights are the cohort sizes). Older cohorts will have little or no bias but more recent ones will and the result is that the overall fatality rate at the point in time still shows some bias. As time marches on, the proportion of all daily cohorts which are more recent also declines so the overall degree of bias reduces.

So I don't think the graphs are reflective of any steady improvement. Rather they are a consequence of the the lifetime of a case being shorter when death rather than recovery is the outcome.

Eventually, the bias will disappear completely and the graphs will converge to an asymptote representing the true fatality rate. I have had a close look at Spain's data and my estimate is around 11%. This represents the case fatality rate (CFR) which is different from the infection fatality rate (IFR).

If I get some time later today or tomorrow I will post some more details.

[zico]

Interesting article on the R-value in Sunday Times. Germany's method of calculating the R-value is to take the number of infections over a 4-day period divided by the number of infections over the previous 4-day period. This means their R-value is transparent to everyone, and also that they can quickly see changes, giving them time to change policies.

By contrast, UK R-value is estimated using a variety of modelling methods, and Jenny Harries said yesterday that there are 3 different R-values for care homes, hospitals, and the general population.
UK probably couldn't use the German method because our testing is far less widespread than theirs, though SAGE may have a like-for-like comparison of daily tests (e.g. only hospitalised cases).

[Itsallaguess]

By contrast, UK R-value is estimated using a variety of modelling methods, and Jenny Harries said yesterday that there are 3 different R-values for care homes, hospitals, and the general population.

Just on that particular point regarding the idea of granular R-values though - doesn't it make a lot of sense to factor those three major areas separately in terms of then being able to compose and prescribe 'Covid-19 management-techniques' differently for each area?

On the face of it, recently walking back slightly on the national UK lock-down protocols at more or less the same time as being told that 'the' UK R-value had perhaps actually ticked up, seemed like strange timing, but if we perhaps consider that the single R-value that we're currently being given 'the range of' might perhaps contain a relatively lower 'general population' R-value that might be getting 'dragged up' by higher care-home and hospital R-values, then the recent combination of those two incidents might perhaps begin to make more sense..

Cheers,

Itsallaguess

[zico]

Just on that particular point regarding the idea of granular R-values though - doesn't it make a lot of sense to factor those three major areas separately in terms of then being able to compose and prescribe 'Covid-19 management-techniques' differently for each area?

I see your point, but it's important to remember R-values are just another way of describing the growth rate in simple terms (so people don't get confused by negative growth rates) so having 3 different ones defeats the point really. As Jenny Harries said, the scale and spread of an epidemic are more important. If we have 3,000 cases per day and an expected increase of 10% per week, in the short-term, that's a lot better than 300,000 cases per day increasing by 1% per week.

If we didn't have R-values, we'd be talking about number of cases and growth rates.

[Mike4]

I seem to remember the scientist types right back at the beginning talking about lockdown being a coarse 'sledgehammer' measure which as weeks and months go by, will get refined. Those comments rapidly vanished from the media bit I think this is what they meant. As testing improves and 'bubbles' of infection get identified along with 'bubbles' of freedom from infection, it makes sense to lock down the bubbles of infection only. The bubbles can be geographical areas, population profiles e.g. elderly, and so on.