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Tired your calculation is wrong, a doubling time of 3 days and a reproduction time scale of 7 days would mean R=5. The modellers mostly used 6.5 days so their value of R=2.4-2.6 was way off. The issue isn't specifically that they had the wrong R, but rather that they had the wrong doubling time. I agree R is less well constrained than the doubling time (given that the time scale is also uncertain) but this fact is well-known by the modellers and R is necessary to estimate the effect of interventions such as social distance and lockdown as these act directly on R rather than doubling time.
Dr J, they were pretty much undone by the publication of SAGE minutes which helped to fill in some extra detail to what I'd worked out prior to that. It helps that my scientific career has focussed on the calibration of numerical models for forecasting (and I'm reasonably good at it) so I did work out what to look at pretty quickly.
But your WW1 analogy is good, because what was expected of the WW1 troops was to make a suicide charge to the German lines in the hope a few would make it, and that is basically what was expected of our care givers and medical professionals.
Think you may have got that slightly wrong. The 'over the top' PBI is the general public.
Medical staff are just collateral damage.
How far would you travel during lockdown?
11,000 miles?
https://www.bbc.co.uk/news/uk-scotland-highlands-islands-52697289
I don’t think he should have, but also… what rule did he break? Lots of people heading back to the UK, and the gov are still ‘discussing’ having quarantine measures for those flying in… no idea why that didn’t start months ago.
Exponential growth rate is (R-1)/generation time and this slope is equal to ln(2)/doubling time. So R is 1 + ln(2)(generation/doubling). 1 + 0.693(7/3) is 2.6. No?
I think the 7 days is bobbins btw. It could be 5 in some places, could be 21 For carriers, and has a distribution that we do not know by country, region, age, gender, etc. By contrast, the Global doubling time was 2.9 days (95% CI 2.7-3.2).
I don't know what the purpose of your calculation is Tired but if R=2.6 and the time scale is 1 week then 1 case turns into 2.6 in a week.
That is simply not doubling in 3 days. One of these cases where being able to produce a (misremembered? misapplied?) formula isn't worth as much as being able to do back of envelope calculations in your head.
Doubling every 3 days is a factor of 5 (almost exactly) in a week.
Anyone want to bet against a scenario where the UK piggy-backs on US bully-boy tactics to obtain vaccines, in exchange for selling of the NHS for a pittance?
Wonder if BoJo's scientists can explain this.
scardypants
Some tempting and unproven vaguely related factors might include:
Older people suffer more from COVID, but women do better than men – look at their osteoporosis prophylaxis (often Ca and VitD)
BAME – darker skins require more uv exposure to make same amount of VitD
Weather generally – we’re coming off winter; Aus/NZ just finished summer so might have higher overall VitD
(… could bring you to lockdown and effects of only 1hr a day outside)(At my place we’re measuring VitD levels in admitted COVID pts – mostly because it’s easy; not part of any formal trial – but not really sure whether we can “help” if/when we find deficiency. We do supplement cancer patients fairly routinely but again, that’s preventitive. As Sandwich’s comment, it’s a bit of a stretch to get to “take this and you’ll waltz off the ICU tomorrow” or even “take this and you’ll never be admitted”)
From a modelling perspective the issue here is inability to segment the data.
e.g. BAME = darker skins require more uv exposure to make same amount of VitD (but that's on average and wide - if you class Berber's with people for whom "black" isn't a stretch both of African to Indian)
I also saw some discussion about poverty but much as we can debate doctors salaries they are not on the breadline and the fatalities in BAME doctors seems unnaturally high.
It's also missing a huge amount of immune system response (does only being mostly homo sapien help or not does the mix of ) or even diet (largely vegetarian/vegan or not are you measuring B12?).
And this is just one side of the model inputs ... what are people dying or not dying of. Who is asymptomatic?
What pre-existing conditions .. and what medication are people on pre-existing conditions taking and how does that correlate with outcomes.
As Sandwich’s comment, it’s a bit of a stretch to get to “take this and you’ll waltz off the ICU tomorrow” or even “take this and you’ll never be admitted”)
It might be stop taking this or that ... or switch to another medication.
It might (and probably will) highlight the at risk groups .. maybe we can't do anything except shield them for now?
As TiRed mentioned early treatment seems best but I feel like we are waiting for symptoms and then treating them. This isn't a surprise in a ICU .. it's what they do and keep people alive but we need to be stopping people needing ICU by early intervention. Anticipate how the virus will affect an individual based on age, gender, haplotype and if necessary diet.
AA
However, medical experts have dismissed those concerns, telling The Sun-Herald the outbreak did not ipso facto show children are susceptible to the virus.
Microbiologist Siouxsie Wiles, head of the Bioluminescent Superbugs Lab at the University of Auckland, said the cluster was named after the school but that did not mean the transmissions all happened there.
Stating the obvious ... and Trivialising and ignoring the actual danger.
"It is not that 100 children and teachers got it," she said. "It's the fact that it spread to their families, that kind of thing."
and missing who did their families spread it to?
In a susceptible-infectious-recovered model, you must factor recovery into the generation process. So rate of new infections is given by
I’ = beta S I - mu I = mu I(beta S/mu - 1),
So (logI)’ = mu(R - 1)
Where beta is contact rate x prob transmission and mu the recovery rate (1/mu is the so-called generation time which is about 7d), R is the basic reproductive number (beta/mu) scaled by proportion susceptible, S. In the early phase everyone is susceptible and S = 1 (it’s probably still pretty close now!)
Hence the basic doubling estimate has to account for loss of infectiousness during the process, that’s the minus 1 part. The naive doubling and generation time doesn’t include this.
Distancing reduces beta, masks may also reduce beta (or reverse if we all mix more), treatments may help increase mu and reduce beta (lower viral load lowers prob of infection/contact). Vaccination definitely lowers S.
And I can’t comment on vitamin D other than to say last year I was tested and had low levels. I took supplements, but not when I was Ill this year, and I was pretty bad. But that’s one case. So I would not take it seriously.
I do think early oxygen supplementation might help with the inflammatory cascade.
https://erj.ersjournals.com/content/42/Suppl_57/P652
Does anyone know if data exists which differentiates between dying from Covid19 and dying with some other issue, eg heart disease plus Covid19 (ie comorbid serious diseases).
That's a lot of algebra, Tired, but I'm not seeing how it addresses whether or not there's a fallacy in thecaptain's simple definition.
The fallacy is in assuming the generations of infection do not overlap. Case 1 infects two other cases, and they each infect two more. If one assumes the average time to infect somebody is half the generation time, then you will find a factor of two.
"If one assumes the average time to infect somebody is half the generation time,"
And we know what they say about assuming things.
That's not what generation time is. It can't be, because most of the total generation time of 6.5d (which was adopted by both of the main modelling groups in the UK) is explicitly considered to be a latent/non-infectious period.
(for the pedants, the latent period may have two slightly different meanings in the literature depending on whether it means asymptomatic or non-infectious, however it's over 4 days under both definitions in the IC model and most others.)
Put it another way, the Ferguson report explicitly states that they use a generation time of 6.5d and R=2.4 and they say their resulting doubling time is 5 days (it's actually 5.1 by my calculation).
Try to square that with your formula.
Try to square that with your formula.
From my point of view it isn't helpful to quote formulae without having defined the terms or the assumptions in the model to which they relate. I'd appreciate an explanation, or else a pointer to an explanation.
If each subject infects R others on average in generation time T, the average time between infections is T/R. Then subtract one for the recovery at the end of the generation time.
I can’t see an error in the Kermack-Mckendrick SIR model - the maths of which have been published for 90 years. The Ferguson model has micro simulation of contacts with stratification, and I’ve no idea how they calculated doubling time on that simulation, presumably stochastic realisations with a distribution.
https://royalsocietypublishing.org/doi/10.1098/rspa.1927.0118#d1285189e1
https://en.m.wikipedia.org/wiki/Compartmental_models_in_epidemiology
The exponential rate of growth is most definitely mu(R-1). One can argue about the interpretation of R and indeed mu, and how one can or cannot derive R from the rate of growth. In the early exponential phase of an epidemic only the product is estimable. Also cumulative cases will have the same exponential rate as new cases.
Anyone got any thoughts on this, seems a bit click baity to me.
I’m aware of the irony
The International Federation of Pharmaceutical Manufacturers and Associations (IFPMA) trade body says companies already share their intellectual property with low-income countries. “We have not been included in these discussions and have limited understanding of what exactly is being proposed, and how it is different from the various institutions already facilitating sharing of data, know-how” and intellectual property, it said in a statement.
Wait till we have some drugs and vaccines.
"If each subject infects R others on average in generation time T, the average time between infections is T/R. Then subtract one for the recovery at the end of the generation time."
Ah, I think I see what you are doing. You seem to be using the infectious interval which will be double the generation time assuming uniform distribution. So that's why your reproduction number is half mine. The meaning of the 6.5d in the literature is certainly as I describe it and a realistic doubling time anywhere close to observations needs a number of 4 or more which is miles away from what the modellers used. Which is why they were talking about 5-7 day doubling right up to 18 March and members of the public were scratching their heads wondering where on earth this "4 weeks behind Italy" thing had come from since we were obviously 2 weeks behind...
Indeed. To estimate T you must convolve with an unknown distribution. Assumptions on that distribution are probably unhelpful. So I think 7days times a delta function is as good as any 😉 . I’m calculating R but think it’s bobbins, personally. Nice to communicate ideas, poor for policy. Basically is the slope of cases, deaths positive or negative. And how has it changed?
I’m happy to report that the correct doubling time (3 days) was communicated on March 16 based on a data-driven analysis. You’ve seen the plots.
Then how come SAGE said it was 5-7d on the 18th? When was this communicated and by who?
thecaptain
Member
Then how come SAGE said it was 5-7d on the 18th? When was this communicated and by who?
Can I ask what difference you feel that doubling time makes to your overall predictions? I beloved it was 3 days doubling in March too although can't remember where I got that information from.
*believed
Anyone got any thoughts on this, seems a bit click baity to me.
You can imagine a scenario where Trump's wet dream is to develop a vaccine in the US, first vaccinate all American (Republican) citizens, then sell it globally at the maximum possible price. Equally, you just know that were the Chinese, say, to develop an effective vaccine, the US would call for it to be made globally available at cost.
Meanwhile were the UK to come up with a viable vaccine, we'd have months of Johnson blathering on about Britain leading the world while in the background we outsourced manufacture to a tiny vitamin pill manufacturer who's aunt happened to be related to some cabinet minister's cousin. Six months later we'd be producing 5,000 doses a month and then failing to send them out, but you'd be able to buy the stuff knock-off on eBay for £10k a shot.
It's depressing that in world with a global economy and minimal effective barriers against international virus spread, that this is even an issue. Gotta love nationalism 🙁
Pharmaceutical drug development and manufacturing is a private enterprise. This situation won't change that. It also won't suddenly negate the need for safe and effective products that are developed and manufactured to appropriate global cGxP.
This situation does create an interesting IP question. I'm not privy to the terms under which Pharma companies are accepting the vast sums of money being thrown around by Governments, but one thing innovative Pharma companies are exceptionally good at is protecting their IP, so we'll just have to see how they are granting rights to the different stakeholders.
one thing innovative Pharma companies are exceptionally good at is protecting their IP
Are they good at protecting it against mass demonstrations or maybe even directly targeted and violent actions? Maybe even state sponsored ones?
If anyone develops an effective vaccine and holds out on it to generate egregious profit I think you will see a very quick escalation from shaming to violence.
This is where nationalism really becomes dangerous. Nation A develops a vaccine but hoards it, giving it to it's own population but holding out on others for economic and/or political reasons. Nation B doesn't have the same facilities but decides a great way to win the everlasting adoration of their public is to...... kidnap a prominent figure from Country A to ransom against access, or bomb the company headquarters of the producer.
Far-fetched?
Maybe, but the recent vogue for populist nationalism makes both country A and country B more likely.
**** populism.
It seems right that vaccine availability is global, but the price should be born by governments, not the private companies. That said, it should be “reasonable profit” not held to ransome.
When was this communicated and by who?
My plots were shown at SPI-M. I have no idea about the decision making. I do know that a collection of models are used to inform decisions, so one piece of information among many.
As for doubling time, in the week before lockdown deaths were doubling every two days in the U.K., which suggested to me that there was an issue with healthcare coping. Cases were still doubling every three days.
In a completely susceptible population, the exponential spread is very predictable. The number of cases needing hospital isn’t hard to guess from this (say 5-10%) nor the number of deaths (1%). Being off by a factor of four is still less than one week. Hence it’s a simple calculation to predict when we would have no ITU beds and scenes like those shown in Italy.
Global availability of the product will depend on several factors - approval of the vaccine at a national level (no such thing as 'global' approval), manufacturing capacity and any pre-existing rights/supply agreements that are tied to the funding/collaboration agreements signed during development.
It's somewhat disheartening that there is still such a wideheld belief that the Pharma industry in general 'withholds' products from any market. Once a company has demonstrated a drug to be safe and effective, and they are able to manufacture it at a commercially viable scale, the process of approval and subsequent reimbursement is a long and complex one. Each country is going to need to come up with its own answer to this. For those countries who lack the infrastructure for effective regulation and the finances for state-sponsored heathcare, I assume we'll see something similar to other mass-vaccination programs e.g. WHO buying and distributing.
It is true that there have been several high profile exceptions of price fixing, such as the case of the 'Pharma Bro' and also the Epanutin epilepsy drug. However, in both cases the responsible parties were rightly punished.
I assume we’ll see something similar to other mass-vaccination programs e.g. WHO buying and distributing.
Thirty years in the making and not for profit.
This is worth a read. Joe Cohen
One would presume something similar for any SARS-COV-2 vaccine too. Countries that can afford to pay will pay more, countries that cannot get the patents or drugs at cost and vaccines via Gavi/WHO. That's how HIV medication works and it helps ensure there are future HIV drugs.
Disclaimer, I work for GSK and am proud to do so. These are my views.
This situation does create an interesting IP question. I’m not privy to the terms under which Pharma companies are accepting the vast sums of money being thrown around by Governments, but one thing innovative Pharma companies are exceptionally good at is protecting their IP, so we’ll just have to see how they are granting rights to the different stakeholders.
I'd guess at a guaranteed percentage of stock manufactured would be yours with other funders getting a percentage that was akin to how much funding they put it. So if Govt A puts in £20m and Govt B puts in £60m and the total cost to develop and get to market is £100m then Govt A gets 20% of the total of each batch, Govt B gets 60% and the pharma company gets to sell the remaining 20% at whatever they can get for it. Extra costs would be incurred by each Govt if they wanted to have someone else manufacture a batch for them via a license. Obviously the clever Govts would agree a price per unit beforehand, the pharma company can make it's profit out of the extra it can sell on the open market.
What will happen is the biggest Govts will try and bully companies into only supplying them, hence Trump's posturing. Unless a parma company decides to make their version available for near-cost price and allow cheap licensing to ramp up production then normal market forces will apply.
Disclaimer, I work for GSK and am proud to do so.
Me too! I don't do anything anywhere near as exciting as you - that's the downsides to Derms products.
We do, however, make this at cost for the WHO https://www.theguardian.com/business/2016/apr/29/glaxosmithkline-antiseptic-gel-prevent-umbilical-cord-infections-eu-approval
And it does save lives. Formulation and manufacturing process are open, so big pharma isn't always bad.
I don't work for big pharma but did used to work in excipient supply to big pharma, and I'm therefore aware at times of the bad press they get.
But the (some would say eye wateringly high) prices that big pharma charge to overindulgent businessmen for drugs to treat their cardiovascular diseases, etc., are why when this happens they can better afford to fund research and offer treatments for the good of all.
TiRed
Being off by a factor of four is still less than one week. Hence it’s a simple calculation to predict when we would have no ITU beds and scenes like those shown in Italy.
Which is ultimately what matters.
Moreover until we have more effective ways to detect/treat/prevent it all seems pointless because we are essentially saying if not this week then next week with a delay distribution we can't accurately define.
Wait till we have some drugs and vaccines.
It seems to me if a vaccine for coronavirus was going to happen it would have been done for the common cold variants/SARS/MERS?
At least the economics for a cold vaccine are not the issue.
It seems more likely from a non expert POV that mitigating the effects in the most vulnerable (once we know who they are) to be the similar to a common cold would be easier and quicker.
It seems to me if a vaccine for coronavirus was going to happen it would have been done for the common cold variants/SARS/MERS?
Common cold coronaviruses - not actually harmful in the overwhelming majority of patients, so no need for vaccines which nearly always carry a very small risk of side-effects etc.
There was significant work on a SARS vaccine which obviously was hampered by the fact that the virus was effectively contained pretty quickly, so they had no humans on which to test its efficacy.
https://www.medscape.com/viewarticle/706717_11
Likewise on MERS, which was continuing even as Covid19 started to emerge.
It seems more likely from a non expert POV that mitigating the effects in the most vulnerable (once we know who they are) to be the similar to a common cold would be easier and quicker
There is still hope for therapies which reduce the severity of the infection, but dialling it down to a sniffle seems very much out of reach.
Re London - reports today of back to near empty tubes and trains again. Did people shit themselves last week and could they - shock horror - be doing the sensible thing?
I rode through Epping Forest car park today and although again it was full of cars it seemed family were very well spaced apart and a Ranger was about- presumably to sort any shenanigans.
Could it be people are being sensible!?
Assuming we can trust the reporting, bad news:
More incompetence:
Please, mummy, make it stop 🙁
Fancy that, a government IT project that isn't working, on time, or on budget.
Not one of those outcomes could be predicted.
Please, mummy, make it stop 🙁
At a number of points in the past few months, I have thought that is the entirety of the government's strategy.
How many projects rushed out in an emergency work straight away ? I mean FFS guys, it's not like the Government people you hate are sitting there typing in Pascal and learning it as they go along.... Come one, lets be sensible for a minute.
If the Gov guy goes into a meeting and says to the Techs, when will this be ready and they say "15th of MAy...." that's all they can go on... But somehow the government are all to blame now ? Come on, reality ?
Losing taste or smell is now officially a reason to isolate in UK.