COVID-19 Coronavirus Containment Efforts

[morrobay]

R0 question: If one infected person infects two in one infection period and those two infect two and those four infect two then after three infection periods there are 2^3 new infections at third infection period. But the total infections are 14. So is the R0 considered 2. Or: (R0)^3 = 14. And 3(logR0)=log14. Then logR0 = .382 . R0=2.4 ?

 

[bhobba]

R0 question: If one infected person infects two in one infection period and those two infect two and those four infect two then after three infection periods there are 2^3 new infections at third infection period. But the total infections are 14. So is the R0 considered 2. Or: (R0)^3 = 14. And 3(logR0)=log14. Then logR0 = .382 . R0=2.4 ?

R0 is the number one person infects each time period and in simple models is considered constant. Roughly it gives a simple differential equation dy/dt = R0*y, y the number infected. The solution is e^(R0*t). It is rough for a number of reasons eg I took it as linear between each period in deriving the differential equation, I did not take into account that infected people are not in the population that can be infected, and people will modify their behaviour as the number of infected grow. Good models are actually not easy to come up with as Oxford discovered with it's original model:
https://www.theguardian.com/science...xposes-the-problems-and-pitfalls-of-modelling

There are, as mentioned in the link above a lot more issues than what I will mention eg you can only really guess some of the parameters involved, but from my reading here are some of the main ones. As a minimum it should be re-run frequently taking into account the current data - which Oxford evidently did not do. Also, it was reported the code for solving the model on a computer was what programmers call 'spaghetti' code eg it has a lot of goto's which makes a program difficult to change and maintain. No goto's was the mantra from day 1 when I studied computing - in fact IMHO no good language should allow it. I have heard however this is not drummed into computing students like it was in my day. Since then recent models are a LOT better eg:
https://engineering.stanford.edu/ma...e-computer-model-predict-how-covid-19-spreads

Thanks
Bill

 

[morrobay]

R0 is the number one person infects each time period and in simple models is considered constant. Roughly it gives a simple differential equation dy/dt = R0*y, y the number infected. The solution is e^(R0*t). It is rough for a number of reasons eg I took it as linear between each period in deriving the differential equation,

Thanks
Bill

Just looking at the math without all the epidemicall variables . Then the R0 like I stated above and you also , is the number of people one infected person transmits infection to in an infection period . Given 3 infection periods ( 12 days/4 day infection period) So three infection periods .Then starting with #1 two infections, #2 four infections , and those four newly infected infect two each. So 8 new infections or 14 total. How does this correspond to e^R0 t. With three infection periods and the R0 in my example being 2. Then the newly infected would be 2^3 or the total for three periods equaling 14. So plugging in: y = e^2*3 = 403 ?

 

[morrobay]

https://en.m.wikipedia.org/wiki/Basic_reproduction_number See chart with ebola R0 = 2 . Then scroll to simple model: new infections(y) = R0^t/infectious period. So with 12 days /4day infectious period then y(t)= 2^3 . Eight new infections . This is just the math I'm looking for because it seems that there is rabbit hole of epidemic variables.

 

[BillTre]

Here is a NY Times opinion article on how the approach of there Biden administration will differ from that of the Trump administration WRT dealing with the Corona virus.

The person in charge of managing the hell out of the operation is Jeff Zients, who served as chief performance officer under President Barack Obama and led the rescue of HealthCare.gov. In a Saturday briefing with journalists, Zients broke the plan down into four buckets. Loosen the restrictions on who can get vaccinated (and when). Set up many more sites where vaccinations can take place. Mobilize more medical personnel to deliver the vaccinations. And use the might of the federal government to increase the vaccine supply by manufacturing whatever is needed, whenever it is needed, to accelerate the effort. “We’re going to throw the full resources and weight of the federal government behind this emergency,” Zients promised.

Most elements of the plan are surprising only because they are not already happening. Biden’s team members intend to use the Federal Emergency Management Agency to set up thousands of vaccination sites in gyms, sports stadiums and community centers, and to deploy mobile vaccination options to reach those who can’t travel or who live in remote places. They want to mobilize the National Guard to staff the effort and ensure that strapped states don’t have to bear the cost. They want to expand who can deliver the vaccine and call up retired medical personnel to aid the campaign. They want to launch a massive public education blitz, aimed at communities skeptical of the vaccine. They’re evaluating how to eke out more doses from the existing supply — there is, for instance, a particular syringe that will get you six doses out of a given quantity of Pfizer’s vaccine rather than five, and they are looking at whether the Defense Production Act could accelerate production of that particular syringe and other, similarly useful goods.

Looks like an improvement to me.

 

[russ_watters]

Here is a NY Times opinion article on how the approach of there Biden administration will differ from that of the Trump administration WRT dealing with the Corona virus.

Looks like an improvement to me.

Is it? It isn't clear to me that it is or should be better. That article is very heavy on opinion and very light on facts, even mis-matching key facts so that the picture of the current situation isn't clear. I've read a bunch of articles about the current situation and still don't think I've seen a clear reason why the roll-out has been so slow or why the current approach should be failing (and not just in the US -- most Western countries seem to be having trouble). So let's start with that.

The Pfizer vaccine was approved in the US on December 11 and the current administration's goal was 20 million innoculations by the end of the year, or a million a day. Plus, presumably, at least a million a day for the first 20 days of January.

The distribution phases are:
1A: Nursing home residents and frontline healthcare workers
1B: Other healthcare workers, essential workers and everyone else over 75.
1C: Everyone else over 65 and high risk people.
2. Everyone else.

https://www.cdc.gov/coronavirus/2019-ncov/vaccines/index.html

Not all states seem to be following this. For example, my state of PA seems to be front-loading phase 1A in their plan, though in reality (based on people I know) it is running more like the CDC's guidance:
https://www.health.pa.gov/topics/disease/coronavirus/Vaccine/Pages/Vaccine.aspx

For the most part, we're still in Phase 1 or just moving to phase 2. So, some obvious/important questions:
1. How many people are in each phase?
2. How many vaccines are avaialble today? Jan 1? Dec 15?

If anyone has that data I'd appreciate sharing, but I'm having trouble finding info on either. But some of the first numbers are available online:
-There are 1.4 nursing home residents in the US. (1A)
-There are 18 million healthcare workers in the US. (1A, though unsure if all are "frontline")
-There are 1.8 million police and fire fighters in the US (1B)
-There are somewhere around 19 million people aged 75 and older. (1B)
-There are somewhere around 36 million people aged 65-74 and older. (1B)
-I have no idea how many "essential workers" and "high risk" people there are. Presumably tens of millions.

So near as I can tell, Phase 1A included just under 20 million people and should have been completed by the new year.
Phase 1B at least another 20 million.
Phase 1C...a hundred million?

The logistical challenges of the different phases are very different from each other. People in 1A are easy to get to and vaccinate using existing infrastructure, so the failure so far is mystifying to me. To vaccinate hospital workers, you just send hundreds of vaccines to thousands of hospitals and they do it themselves. To vaccinate nursing home residents and staff, you send the vaccines to whatever healthcare partner (often pharmacies) already does their mass-vaccinations. From what I've seen and heard from my friends/family, that's happened. So, why the numbers don't bear-out a larger total is confusing. This article (a week old) implies that it is the states that are having trouble:

However, the distribution of vaccines has gotten off to a slower-than-expected start, with millions of doses distributed to states but sitting unused in freezers.

https://www.healthline.com/health-news/why-the-covid-19-vaccine-rollout-is-so-slow

This says the federal guidelines have been relaxed to open up all of the first three phases and make 250 million people eligible:
https://www.webmd.com/vaccines/covi...dy-to-supply-covid-19-vaccines-to-americans#1

In addition, the 40,000 chain drug stores in the US have the capacity to administer about 3 million a day. Then there's hospitals, urgent care centers, doctors offices.

Back to the original article:

Set up many more sites where vaccinations can take place. Mobilize more medical personnel to deliver the vaccinations.

It's a major pandemic so I favor an all-hands-on-deck apprach and x+1>x, so it is trivial to say that that's "better", but I don't see why it should have been necessary so far to achieve the goal. It looks to me like our existing capacity should already have vastly outperformed the goal.

And use the might of the federal government to increase the vaccine supply by manufacturing whatever is needed, whenever it is needed, to accelerate the effort.

That's pretty vague. How does the government do that and how long does it take?

The new administration's goal is 100 million vaccines in 100 days, or exacly the same as the last one, even with hindsight and 40 days of ramp-up. To me, that's a pretty underwhelming goal. There's two ways to look at that: either the new goal is pessimistic and we should do a lot better or the old goal was overly optimistic and we should have expected it to be as slow as it was (or somewhere in between).

 

[russ_watters]

Is it? It isn't clear to me that it is or should be better. That article is very heavy on opinion and very light on facts, even mis-matching key facts so that the picture of the current situation isn't clear.

Here's the mismatch:

According to data from the Centers for Disease Control and Prevention, of the roughly 31 million doses that have been sent out, about 12 million have been used.

On its own, this doesn't tell us anything at all about any sort of problem because we don't know where the remaining 19 million doses are. If they're expired and in a trash can, that's a failure. If they're in a refrigerator to be administered tomorrow or in shipping a shipping container on a truck, then they're somewhere in the supply chain and there isn't necessarily an issue. And maybe more have been vaccinated if there is a lag in reporting the vaccinations. But the numbers are as of January 15, so we can say that the total shipped is below the roughly 35 million that should have been administered by now. So it would seem that too few have shipped (even fewer if you consider that they couldn't pre-stage the vaccine and only started shipping the day after approval). So, what is causing that bottleneck?

This article discusses bottlenecks at the state, federal and manufacturing level, but doesn't make it clear if those bottlenecks cascade up (e.g. if the state bottleneck caused the federal bottleneck):
https://www.nytimes.com/2020/12/17/health/pfizer-covid-vaccine-doses.html

 

[bhobba]

Then the newly infected would be 2^3 or the total for three periods equaling 14. So plugging in: y = e^2*3 = 403 ?

It's in deriving the differential equation. The time period you used is discreet. To get the differential equation let us say the time period is a day. To get to an infinitesimal time period you assume during that one day it is linear (it isn't really but it is a simplifying assumption). The detail is using a one day R0, the increase over 1 day is R0*y where y is the current number of cases. Making the simplifying assumption it is linear, over half a day it is R0*1/2*y, over an infinitesimal period dt it is R0*dt*y. So you get after an infinitesimal time period of dt the increase, dy, is R0*dt*y. So one gets dy/dt = R0*y. Why it does not give your numbers is in deriving the equation we assume it is linear during that one day period. It isn't really, so you do not get the same numbers as your discreet calculation. You could get the R0 (R0') over an infinitesimal period from solving e^(R0') = 1+R0 or R0' = Ln(1+R0). That would be a more refined model. Ln = Log to base e. It still will not give your discreet values because you are assuming a continuous infection rate instead of a discreet one. It would have been better to express your infection rate in terms of an infinitesimal time period to start with so after dt the new number of infections is y + R0*y*dt. For your 3 days the infinitesimal R0, R0' would be e^(R0'*3) = 1 + R0 or R0' = (ln (1 +RO))/3. This is similar to the concept of force of interest in finance:
https://en.wikipedia.org/wiki/Compound_interest

Thanks
Bill

 

[BillTre]

That article is very heavy on opinion and very light on facts, even mis-matching key facts so that the picture of the current situation isn't clear. I've read a bunch of articles about the current situation and still don't think I've seen a clear reason why the roll-out has been so slow or why the current approach should be failing (and not just in the US -- most Western countries seem to be having trouble). So let's start with that.

Well, it is an opinion article (as I clearly labeled it).

However, I think the main issue is that data stream of US government info on the corona virus has been corrupted and the data are not dependable.
This is likely also true with Florida data.

I expect different numbers to become available a week or two.

 

[russ_watters]

Well, it is an opinion article (as I clearly labeled it).

Yes, I know. Doesn't mean I need to be happy abou/agree with the value of such a low quality source.

However, I think the main issue is that data stream of US government info on the corona virus has been corrupted and the data are not dependable.

This is likely also true with Florida data.

I expect different numbers to become available a week or two.

I don't know what you mean by that. What data are you referring to? That sounds vaguely like conspiracy theory.

More to the point, "different numbers" does not fix the logic problem in the media reporting mismatched statistics.

 

[PeroK]

To change the subject, here's an interesting thing.

1) From last Friday morning, flights from Portugal (in addition to S America) to the UK were halted because of fears of a new variant, originating in Brazil and likely to have spread to Portugal.

2) The Portugese Foreign Minister described it as "absurd".

https://www.reuters.com/article/hea...ortuguese-foreign-minister-says-idUSL8N2JQ2G7

3) Today, Portugal (a country of 10 million people) has reported nearly 15,000 cases and 219 deaths. And, it's been about 10,000 cases a day for about 10 days now.

This shows that some governments are still being wholly unrealistic about the extent to which the virus is hitting their country and the threat to other countries posed by international travel.

 

[BillTre]

I don't know what you mean by that. What data are you referring to? That sounds vaguely like conspiracy theory.

Well, I am trying to avoid going into politics, by not responding directly to your challenge(s),
so I won't cite specific causes (also, making my job easier).
In addition, I will avoid providing long explanations that could be portrayed as a conspiracy theory.

But, I will make predictions:

• the numbers of vaccines produced will be revised down
• estimates of numbers (cases, deaths, hospitalizations) associated with the corona virus, will be changing (but this could (will?) be attributable to changes in calculations)
• the federal vaccine back-up supplies will be shown to have been vastly over-estimated and over-hyped
• weird reasons for not doing obvious things will be revealed (some will involve corruption ($'s))

I expect these things will begin to happen within a couple of weeks. Some maybe faster, some slower.
Check back with that latency.

I have, to a large extent, come to be not be so interested in all the corona virus numbers, because I think there are too many problems with them.
Besides the normal causes of uncertainty and differences between states, there are clear indications of politicians messing (which I am not going to go into here (too political, but you can goggle them up for yourself)) with the numbers, thus corrupting them for predictive purposes.

If the data you are using is not good, then your calculated numbers will not make sense.

 

[nsaspook]

https://www.sfgate.com/coronavirus/...-dining-ban-COVID-19-surge-worse-15882565.php

Late last week, Chicago mayor Lori Lightfoot — typically cautious on COVID-19 policy — raised some eyebrows after calling for restaurants and bars to reopen "as soon as possible."

Her logic: The current COVID-19 surge has been primarily fueled by at-home gatherings and parties, and if people are going to gather regardless of what any stay-at-home order dictates, state and local governments should try to provide spaces where at least some mitigation efforts will be taken.
...
Despite the ban, California has had one of the worst winter COVID-19 surges in the country, which begs the following question: Is it possible that shutting down outdoor dining made the state's surge even worse?Dr. Monica Gandhi, an infectious disease expert at UCSF, believes it's highly likely.

"We won’t be able to know the exact percentage it drove, but I would say closing outdoor dining certainly did not help and likely hindered efforts to avoid a surge," she said. "It shut down in early December, and things did not get better from there; things actually got worse. Restrictions should be about understanding the human condition and keeping places that are safe open. Those of us who argue for a harm reduction approach have the same goal as the lockdownists: We want to reduce transmission, but we understand the human condition and the need to be with people."

Locally there has been a risk mitigation reevaluation of dining rules.

 

[russ_watters]

But, I will make predictions:

• the numbers of vaccines produced will be revised down
• estimates of numbers (cases, deaths, hospitalizations) associated with the corona virus, will be changing (but this could (will?) be attributable to changes in calculations)
• the federal vaccine back-up supplies will be shown to have been vastly over-estimated and over-hyped
• weird reasons for not doing obvious things will be revealed (some will involve corruption ($'s))

I expect these things will begin to happen within a couple of weeks. Some maybe faster, some slower.
Check back with that latency.

I have, to a large extent, come to be not be so interested in all the corona virus numbers, because I think there are too many problems with them.
Besides the normal causes of uncertainty and differences between states...

Well, fair enough, but I thought we were in a narrowly focused discussion of the vaccine roll-out. I'm not real interested in case rates for this discussion either.

As far as I can tell, there are no running tallies of vaccine production. The most detail I've seen is from Pfizer, which 6 weeks ago reduced its 2020 global production target from 100 million to 50 million doses, and I don't even know how many were allocated, much less shipped, to the US:
https://time.com/5917847/pfizer-cut-covid-19-vaccine-targets/
https://www.npr.org/2020/12/18/9480...es-are-ready-but-states-say-shipments-were-cu

There's finger-pointing right now, but because the vaccines direct-ship from the manufacturer to the states or users (not through a federal government distribution center), we don't actually have a window into their production volumes and delivery capabilities. There's no way for us to know if there are millions of doses sitting ready for shipment with no address to send them to or if they are struggling to keep the warehouse stocked for shipping. But the admission that they halved their production target tells me that the largest bottleneck is probably in production, not distribution or innoculation.

But I guess we'll see. About all of that.

 

[morrobay]

It's in deriving the differential equation. The time period you used is discreet. To get the differential equation let us say the time period is a day. To get to an infinitesimal time period you assume during that one day it is linear (it isn't really but it is a simplifying assumption). The detail is using a one day R0, the increase over 1 day is R0*y where y is the current number of cases. Making the simplifying assumption it is linear, over half a day it is R0*1/2*y, over an infinitesimal period dt it is R0*dt*y. So you get after an infinitesimal time period of dt the increase, dy, is R0*dt*y. So one gets dy/dt = R0*y. Why it does not give your numbers is in deriving the equation we assume it is linear during that one day period. It isn't really, so you do not get the same numbers as your discreet calculation. You could get the R0 (R0') over an infinitesimal period from solving e^(R0') = 1+R0 or R0' = Ln(1+R0). That would be a more refined model. Ln = Log to base e. It still will not give your discreet values because you are assuming a continuous infection rate instead of a discreet one. It would have been better to express your infection rate in terms of an infinitesimal time period to start with so after dt the new number of infections is y + R0*y*dt. For your 3 days the infinitesimal R0, R0' would be e^(R0'*3) = 1 + R0 or R0' = (ln (1 +RO))/3. This is similar to the concept of force of interest in finance:
https://en.wikipedia.org/wiki/Compound_interest

Thanks
Bill

Thanks, The compound interest formula, final=initial (1+%)^n is exactly how I am solving for the R0 from initial and final infections: 17(R0)^6 = 231. Then (R0)^6=13.58 and 6(logR0) = log 13.58. therefore log R0 =.1888 so R0 is 1.54 I just am asking if this is valid for solving R0. Note 6 infection periods from 24 days/4 day max.infectious period from initial infection.

 

[bhobba]

Thanks, The compound interest formula, final=initial (1+%)^n is exactly how I am solving for the R0 from initial and final infections: 17(R0)^6 = 231. Then (R0)^6=13.58 and 6(logR0) = log 13.58. therefore log R0 =.1888 so R0 is 1.54 I just am asking if this is valid for solving R0. Note 6 infection periods from 24 days/4 day max.infectious period from initial infection.

OK then let's go carefully through the math. We want to find the infinitesimal R0 similar to the force of interest idea for compound interest. You are using that after 6 days on the average 1 person infects 13.58 people. So we know that e^(6*R0) = 1+ 13.58 = 14.58. This means 6*R0 = ln 14.58 = 2.68 or R0 = 2.68/6 = .45 to two decimal places. You just need to understand the concepts involved which is largely basic differential equations and really everyone should be taught it at HS. They have wide applicability in many situations - infection spread and compound interest are just two. It allows one to think clearly about concepts like R0 and compound interest rates. This is done by treating time as continuous and working in terms of parameters based on doing that. People sometimes say - how do we know time is continuous. The answer is we do not. By modeling situations as if it is we can use calculus which allows progress to be made in a clear and precise way. As you probably know there is all sorts of philosophical ideas about what science is - Wittgenstein, Kuhn, Popper, Poincare, Feynman (he was sort of anti-philosophy - which interestingly is a philosophy in itself) etc. I recently read a book on an introduction to the subject that examined carefully a number of different views. It glossed over a view called the modelling view saying not a lot of work has been done on it. Philosophers might not have done a lot of work on it, but mathematicians and scientists use it all the time, and IMHO it is the correct view - but that is another story not really suited to this forum.

On another forum a question was once posed - before leaving school what is the most important thing students should understand. My answer was basic calculus. I was laughed at. But you have just witnessed how it resolved the confusion you had about R0. Another good one is if you go a bit further than basic calculus into real analysis (where calculus is studied with full logical rigor and not intuitive ideas like an infinitesimal period of time dt) and use it on Zeno's paradoxes. The solution is then clear. One of the fundamental axioms of real numbers often used in real analysis is the Least Upper Bound Axiom (LUB). It says - Every non-empty subset of real numbers that is bounded above has a least upper bound. In modelling the tortoise and hare race by real numbers the LUB axiom applies. Now obviously it has an upper bound where the race has finished. But we know there is a least upper bound. Below that the race is still going, above it, it has finished. So that must be when the race ends. Many many people, and some even post here about it, are totally unaware of this and think it is still unsolved. Some people think even the calculus explanation does not solve it - you really need physics.
https://www.forbes.com/sites/starts...esolves-zenos-famous-paradox/?sh=6ed441b033f8

But we are now getting way off topic - if you want to pursue it further then start a new thread.

Thanks
Bill

 

[mfb]

But the admission that they halved their production target tells me that the largest bottleneck is probably in production, not distribution or innoculation.

These don't exclude each other. The bottleneck can be the distribution even though the production might be a bit lower than planned. Is it really lower? The 50 million in 2020 has been a target for quite some time.

Concerning the R0 discussion: You are all missing that people are not infectious the second after getting infected. The linear model with the timescale of the incubation period is better here, a modified exponential function will work as well.

 

[morrobay]

OK then let's go carefully through the math. We want to find the infinitesimal R0 similar to the force of interest idea for compound interest. You are using that after 6 days on the average 1 person infects 13.58 people. So we know that e^(6*R0) = 1+ 13.58 = 14.58. This means 6*R0 = ln 14.58 = 2.68 or R0 = 2.68/6 = .45 to two decimal places. You just need to understand the concepts involved which is largely basic differential equations and really everyone should be taught it at HS. They have wide applicability in many situations - infection spread and compound interest are just two. It allows one to think clearly about concepts like R0 and compound interest rates. This is done by treating time as continuous and working in terms of parameters based on doing that. People sometimes say - how do we know time is continuous. The answer is we do not. By modeling situations as if it is we can use calculus which allows progress to be made in a clear and precise way. As you probably know there is all sorts of philosophical ideas about what science is - Wittgenstein, Kuhn, Popper, Poincare, Feynman (he was sort of anti-philosophy - which interestingly is a philosophy in itself) etc. I recently read a book on an introduction to the subject that examined carefully a number of different views. It glossed over a view called the modelling view saying not a lot of work has been done on it. Philosophers might not have done a lot of work on it, but mathematicians and scientists use it all the time, and IMHO it is the correct view - but that is another story not really suited to this forum.

On another forum a question was once posed - before leaving school what is the most important thing students should understand. My answer was basic calculus. I was laughed at. But you have just witnessed how it resolved the confusion you had about R0. Another good one is if you go a bit further than basic calculus into real analysis (where calculus is studied with full logical rigor and not intuitive ideas like an infinitesimal period of time dt) and use it on Zeno's paradoxes. The solution is then clear. One of the fundamental axioms of real numbers often used in real analysis is the Least Upper Bound Axiom (LUB). It says - Every non-empty subset of real numbers that is bounded above has a least upper bound. In modelling the tortoise and hare race by real numbers the LUB axiom applies. Now obviously it has an upper bound where the race has finished. But we know there is a least upper bound. Below that the race is still going, above it, it has finished. So that must be when the race ends. Many many people, and some even post here about it, are totally unaware of this and think it is still unsolved. Some people think even the calculus explanation does not solve it - you really need physics.
https://www.forbes.com/sites/starts...esolves-zenos-famous-paradox/?sh=6ed441b033f8

But we are now getting way off topic - if you want to pursue it further then start a new thread.

Thanks
Bill

Hello, I am not calculating for the infinitesimal R0 , rather the basic one IE ranging from 1 to 3 for example. Also the 6 above are the infection periods from 28days/4 day infectious period. So with R0=e^Kt , with K = ln2/Td (exponent of growth) We have ln2/6 = .1155 and t=4days, the infectious-serial interval. So the R0=e^.462 equals 1.58. https://en.m.wikipedia.org/wiki/Basic_reproduction_number Scroll to simple model for reference to above

 

[bhobba]

Concerning the R0 discussion: You are all missing that people are not infectious the second after getting infected. The linear model with the timescale of the incubation period is better here, a modified exponential function will work as well.

Indeed the model is very simplistic and false. It was just used to show that R0 as the average number of people an infected person infects is best taken over a small time period. It will change with time of course due to people being infected, modifying their behaviour etc.

Thanks
Bill

 

[bhobba]

Hello, I am not calculating for the infinitesimal R0 , rather the basic one IE ranging from 1 to 3 for example. Also the 6 above are the infection periods from 28days/4 day infectious period. So with R0=e^Kt , with K = ln2/Td (exponent of growth) We have ln2/6 = .1155 and t=4days, the infectious-serial interval. So the R0=e^.462 equals 1.58. https://en.m.wikipedia.org/wiki/Basic_reproduction_number Scroll to simple model for reference to above

Ahhhhh. Sorry, I misinterpreted what you were saying. I think further discussion of R0, should take into account the specific model being used as per the link you gave: 'R0 can be calculated from many different mathematical models. Each of these can give a different estimate of R0, which needs to be interpreted in the context of that model.' The main point I was trying to make is in the simple, but unrealistic, model I used for illustration, it needed to be the number of people infected in a small or infinitesimal time period.

Thanks
Bill

 

[morrobay]

Yes the R0 certainly is a flexible term

 

[bhobba]

Yes the R0 certainly is a flexible term

That I now realize clearly. Much appreciation for the link you gave - it made clear something I should have known for the start. You live and learn.

Thanks
Bill

 

[PeroK]

That's an argument that the CDC 0.26% number is wrong. That's a position that's defensible, but should be attacked on it's merits.

I thought it was worth returning to this question now that we have more data. The question was whether the eventual maximum death rate for COVID, as estimated by the CDC, would be about 0.26%.

The current data for New Jersey is about 0.23%. Unless there is almost no one left in NJ who could die from COVID then this estimate must have been wrong in some way.

The current estimate in the UK is that perhaps 15% of the population has had COVID (about 10 million people) and we've had nearly 100,000 deaths. This gives an estimate of up to 1% eventual deaths - which is, in fact, in line with the original estimate of up to a maximum of 500,000 deaths in the UK.

 

[morrobay]

Concerning the R0 discussion: You are all missing that people are not infectious the second after getting infected. The linear model with the timescale of the incubation period is better here, a modified exponential function will work as well.

Yes, typically symptoms appear 4 or 5 days after exposure. Emerging research suggests that people are most likely to spread virus 48 hrs before symptoms.* So the max infectious period or serial interval is about 4 days into initial infection. And that is how the exponent of growth of 6 in post #4603 was given: 24days/4day serial interval. In that post 24 days not 28, but does not alter end result. * https://www.health.harvard.edu/diseases-and-conditions/if-youve-been-exposed-to-the-coronavirus

 

[russ_watters]

These don't exclude each other. The bottleneck can be the distribution even though the production might be a bit lower than planned. Is it really lower? The 50 million in 2020 has been a target for quite some time.

I don't know what "quite some time" means to you. According to the source I linked, it was somewhere around December 1. To me, losing half / 50 million doses in a month - your only month - is a big change in a short time.

And sure, there can be more than one bottleneck, but if the bottle itself is too small, eliminating the bottlenecks still won't enable achieving the goal.

[edit; expanding]
The slow ramp-up of the first 20 (+20) days surely must have been distribution issues. The number of doses delivered seems just way too small too have been caused by production delays, particularly because there was some stockpiling prior to the vaccine's approval. But if the inoculation goal for the next 100 days is realistic, that's a much, much bigger problem. It's saying that no additional ramp-up in inoculation rate is possible at this time. That has to be production limited because it's just too easy to perform a million inoculations per day.

Selfishly, my goal here is to project when I might get inoculated (the other 3 people in my COVID circle will all have their first dose by this weekend). Before I incorporated the new goal into my thought process, I was thinking primarily about our inoculation capacity, and I had hope that the rate would continue to ramp up. I was speculating we might get to the point where I could receive my first dose in March or April.

I'm not sure I really went through the numbers like this before, but say the December goal was 1 million a day, and each month added another million a day in ramp-up. That would be 440 million doses by the end of April.

Now it looks like we won't even be 1/4 of the way there. The current goal of 1 million a day for the next 120 days is roughly 120 million doses administered by April 20, and my source above said the first three groups comprise about 250 million people. So given the two-dose requirement, that's a little less than 1/4 of the way through the people in line ahead of me.

 

[russ_watters]

Here's the vaccine distribution and dosing data, pulled from the CDC website via wayback machine:

The data is a little sparse, but it appears to show the rate of doses administered is ramping-up while the rate of doses distributed is ramping-down. The per day rates from one point to the next are too noisy to show much when close together, but the overall averages for the past 18 days are 1.27 million per day distributed and 0.68 million per day administered. The last two points give an average over the past 5 days of 0.97 million per day distributed and 0.85 million per day administered.

Source:
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/index.html
Caveat: A couple of weeks ago, the statistics changed from "total receiving first dose" to "total administered". But since I doubt many people had received a second dose by the 1st week in January, that shouldn't skew the data much.

I'd like to see the numbers for December (particularly since the "administered" curve doesn't seem to point toward zero), but alas, the site doesn't seem to have that data. I'll look for other sources and fill-in if I can.

 

[mfb]

I don't know what "quite some time" means to you. According to the source I linked, it was somewhere around December 1. To me, losing half / 50 million doses in a month - your only month - is a big change in a short time.

The 50 million number is much older, and even your source is saying that. Here is a November 9 press release expecting 50 million in 2020.
The time.com article says the 100 million estimate was made in September. The npr article doesn't discuss a 100 million in 2020 estimate.

The slow ramp-up of the first 20 (+20) days surely must have been distribution issues. The number of doses delivered seems just way too small too have been caused by production delays, particularly because there was some stockpiling prior to the vaccine's approval. But if the inoculation goal for the next 100 days is realistic, that's a much, much bigger problem. It's saying that no additional ramp-up in inoculation rate is possible at this time. That has to be production limited because it's just too easy to perform a million inoculations per day.

If it's so easy, why isn't it done? The deliveries exceed the administered doses massively. That's incompatible with deliveries being the bottleneck. Based on your graph there are 20 million doses somewhere that have been delivered but not being used yet. More than the total number of doses given to people. You expect some of these doses to be in the delivery chain, obviously, but not that many. At the current inoculation rate they have vaccines for over a month sitting somewhere in freezers. The Pfizer/BNT vaccine doesn't even last that long while it's deeper down the delivery chain: If these doses don't end up being thrown away then they are in deep freezers at a few central locations waiting for ... I don't know what.

Israel had a surge of new cases while it was rapidly starting vaccinations (at a record per capita rate). New case numbers seem to have stabilized now. It's unknown how much of that is due to vaccination and how much is due to other measures, however. 37 doses given per 100 people, but some of them should be the second dose by now, so the fraction of vaccinated people will be lower. If we assume ~2 weeks before the vaccine is effective then we have ~20% of the population with protection against the virus. These are unlikely to become confirmed cases, how likely they are to get infected is less clear.
Israel is on track to have vaccinated half of its population (100 doses per 100) by the end of March, and everyone who wants the vaccine within the first half of 2021.

 

[bhobba]

If it's so easy, why isn't it done? The deliveries exceed the administered doses massively.

Here in Aus everyone is saying delivery will not be a problem - it is administering it - especially the Pfizer vaccine since where it is administered needs special storage facilities. Scheduling people to come in and get it at places geared up for it (usually main hospitals - rural ones do not have the facilities) is a logistical nightmare. Normally you just make an appointment with your GP and pop into get the vaccine. But GP's are not geared up to store it. Things will be better with the Oxford vaccine where the normal method would still work. But getting everyone to go to their GP is still a time consuming undertaking - especially with the two tiered system we have. Some GP's charge the recommended fee (the fee recommended by the Royal College of Australian General Practitioners) and you pay the difference between that and a government payment. At others called bulk billers you pay nothing, and the doctor just gets the government fee. Mine is sort of halfway between. My doctors have a good relationship with their patients and know their financial circumstances. They decide whether to charge the full fee or bulk bill depending on circumstances. For example when my sister worked she paid full fee. When she got sick and could no longer work, plus had children to raise, she and her family were bulk billed. When the children left home they started charging her full fee, which she did not like so she went to a bulk biller. There are fewer of those, and she has to wait a few days for an appointment, whereas with mine you can always get in on the same day - although it may not be with your regular doctor. Bottom line is getting the people through the GP's can take time, especially if you see a bulk biller. The solution being looked at is, at first the vaccinations will only be done by doctors so they can handle any adverse reaction should one occur. Once it proves itself, then any chemist or facilities that will be set up by the government manned by nurses will be able to do it. At least that is the current thinking. The government is still thinking through about what to do at places like Alice Springs with the Pfizer vaccine - they could deliver it there easy enough - but storing it etc is another matter.

Thanks
Bill

 

[mfb]

For illustration, here is the number of delivered vaccines shifted by 2 weeks. I added two older data points (23rd and 29th December). I tried to find Dec 18 but the CDC page didn't have a vaccine tab that day. In the first half of January the US had two weeks time between delivery and admitting the dose. That sounds like a realistic delay you expect from logistics, so at that time the US could have been limited by supply. Then deliveries ramped up in early January, but that increase didn't lead to a faster rate of vaccinations yet: Looks like the vaccination rate had a similar limit as supply before.

 

[russ_watters]

The 50 million number is much older, and even your source is saying that. Here is a November 9 press release expecting 50 million in 2020.

Ok, you're right; the the report I was looking at was from December 3 but said "in recent weeks". Anyway, I don't want to get bogged down in the "when" of those projections. My point here is that I don't think the 20 million injections in 2020 goal was possible and that manufacturing and distribution (but not administration) were what constrained it.

[skipping ahead]
For illustration, here is the number of delivered vaccines shifted by 2 weeks. I added two older data points (23rd and 29th December). I tried to find Dec 18 but the CDC page didn't have a vaccine tab that day. In the first half of January the US had two weeks time between delivery and admitting the dose.

Ok, thanks, I guess I wasn't persistent enough with the archive. It gets spotty/unreliable back then, but I was able to find data for the 21st and 28th, and an "administered" number from the 18th. The first doses shipped on Dec 13 and first inoculation was Dec 14. Here's an updated graph, with the best time-shift fit being 16 days:

That sounds like a realistic delay you expect from logistics, so at that time the US could have been limited by supply.

Agreed. The ramp-up in "administered" before matching the slope of the "distributed" curve looks like what you'd expect from filling a distribution pipeline. Maybe they can shrink that delay, but since this is a year-long effort I'm not two concerned about a 2-week lag becoming a 1-week lag. So, yes, I agree that this looks like limited supply, and that's what worries me.

Then deliveries ramped up in early January...

"Distributed" means shipments, not deliveries. The start of the distribution pipeline, not the end (when I used the word "deliver" earlier, I meant delivery to the final destination: an arm). But yes, there has been some ramp-up of that; from about 500,000/day in the third week in December to 1.5 M/day today. Note, the Moderna vaccine started shipping on Dec 20.

What I'm not seeing in the "distributed" data is any evidence of a day 1 stockpile. Unfortunately I only have the first 8 days (the 12/18 is a fake point I added to avoid a discontinuity), but what it tells me is if there was a stockpile, it couldn't have been more than a couple of million doses. E.G., if there was a 7 million stockpile, I would have expected it to be shipped in the first week, showing a million a day for the first week, then dropping to the half million a day production rate the second week.

[back to the prior post]
If it's so easy, why isn't it done? The deliveries exceed the administered doses massively. That's incompatible with deliveries being the bottleneck. Based on your graph there are 20 million doses somewhere that have been delivered but not being used yet.

We might already be past this, but just to make sure it's clear: the data says "distributed", not "delivered". Maybe you are using "delivered" to mean delivered from Pfizer to the supply chain, but that's an odd way to put it since they are shipping from Pfizer. In other words, those 20 million doses are somewhere in the supply chain, having been shipped (distributed) from Pfizer, but not yet delivered (administered) to an arm. That's the 16 day lag. Note: that also includes any reporting delay.

I'm typing this while watching the noon news, and they're interviewing directors of mass injection sites who are saying they are having to cancel appointments because not enough vaccine is being delivered to them.

 

[russ_watters]

Here in Aus everyone is saying delivery will not be a problem - it is administering it - especially the Pfizer vaccine since where it is administered needs special storage facilities. Scheduling people to come in and get it at places geared up for it (usually main hospitals - rural ones do not have the facilities) is a logistical nightmare. Normally you just make an appointment with your GP and pop into get the vaccine.

Here in the US many people get the flu vaccine from their GP, but tens of thousands of chain pharmacies also administer them for free. A small practice could dedicate one nurse and exam room, and administer a hundred a day.

But GP's are not geared up to store it.

I don't think that's as big an issue as many people think -- I feel like people think every vaccination site needs a -80C freezer. They don't. The shelf life is 5 days in a normal refrigerator, and the shipping container is good for 30 days if you keep re-filling it with dry ice. So as long as you can source dry ice and have a normal refrigerator for today's doses, there's not really any difficulty. I'd sure hope they can administer them fast enough that they don't need to keep them in the shipping container or refrigerator very long.
https://www.pfizer.com/news/hot-topics/covid_19_vaccine_u_s_distribution_fact_sheet#:~:text=After storage for up to,or stored under frozen conditions.

 

[nsaspook]

Speaking alongside Johnson on Friday, the U.K.’s chief scientific advisor, Patrick Vallance, said there is now early evidence that there’s an increased risk for those who have the new variant, compared with the old virus.

“If you took ... a man in their 60s, the average risk is that for 1,000 people who got infected, roughly 10 would be expected to unfortunately die with the virus. With the new variant, for 1,000 people infected roughly 13 or 14 people might be expected to die,” Vallance said.

He described the data as not being strong yet, and highlighted more concern regarding other Covid variants found in Brazil and South Africa.

https://www.cnbc.com/2021/01/22/bor...ariant-associated-with-higher-mortality-.html

Not good news.

 

[Astronuc]

Apparently PM of UK Boris Johnson made a comment that the new variant in the UK may be more deadly, but that is not yet clear.

“In addition to spreading more quickly, it also now appears that there is some evidence that the new variant … may be associated with a higher degree of mortality,” Johnson said Friday afternoon during a press briefing.

Chief scientific adviser, Sir Patrick Wallace, added that the variant transmits 30% to 70% more easily, but there is no understanding of the reason yet, and there isn’t strong enough data to confirm the variant is, in fact, more deadly.

Wallace said the news about the virus being deadlier was based on looking at overall data, compared to just hospitalized patients. Hospitalized patients are not dying at increased rates with the new variant versus the old.

https://finance.yahoo.com/news/coro...ays-second-dose-can-be-delayed-195502095.html

At a White House briefing Thursday, Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said vaccines are likely to still be effective against B.1.1.7 and the variant from South Africa, 501Y.V2, which has not yet been reported in the U.S.

On a positive note, my wife got the first shot of the Pfizer vaccine today, and is scheduled for the second shot in 3 weeks. I won't be eligible for several more months.

 

[Cobul]

I heard in the news last year that the flu killed millions a year in the US alone and tens of millions worldwide. Why didn't we have lockdown for flu? Is it due to the Covid being new so people were more afraid or excited? Does it mean when people get used to Covid and it kills millions a year in the US, it would be as common as the flu and people would accept it, and slowly we won't keep hearing it at headlines like the flu and get used to it?

 

[Jarvis323]

I heard in the news last year that the flu killed millions a year in the US alone and tens of millions worldwide. Why didn't we have lockdown for flu? Is it due to the Covid being new so people were more afraid or excited? Does it mean when people get used to Covid and it kills millions a year in the US, it would be as common as the flu and people would accept it, and slowly we won't keep hearing it at headlines like the flu and get used to it?

No, in the last decade, the Flu has been causing between 12-60k estimated deaths per year in the US.

I bolded estimated, because those numbers are not the recorded number of deaths (which are much lower), they are the estimated number of deaths, which are inferred based on mathematical models. We still don't know what the ultimate estimated number of Covid-19 deaths will be at this point, but if estimation goes like it does for the Flu, then the number of Covid-19 deaths will go up drastically. For the Flu, they sometimes end up with numbers 2-4 times higher than what they have direct records of. In other words, the actual recorded Flu deaths are more in the range of 3k to 30k in the US.

If similar inflation of the deaths after estimation occur with covid-19, then it would mean we are at more like 800,000 to 1,600,000 deaths in the US right now. But who knows what will happen. This is an unprecedented situation.

Why doesn’t CDC base its seasonal flu mortality estimates only on death certificates that specifically list influenza?

Seasonal influenza may lead to death from other causes, such as pneumonia, congestive heart failure, or chronic obstructive pulmonary disease. It has been recognized for many years that influenza is underreported on death certificates. There may be several reasons for underreporting, including that patients aren’t always tested for seasonal influenza virus infection, particularly older adults who are at greatest risk of seasonal influenza complications and death. Even if a patient is tested for influenza, influenza virus infection may not be identified because the influenza virus is only detectable for a limited number of days after infection and many people don’t seek medical care in this interval. Additionally, some deaths – particularly among those 65 years and older – are associated with secondary complications of influenza (including bacterial pneumonias). For these and other reasons, modeling strategies are commonly used to estimate flu-associated deaths. Only counting deaths where influenza was recorded on a death certificate would be a gross underestimation of influenza’s true impact.

https://www.cdc.gov/flu/about/burden/how-cdc-estimates.htm

In other words, we've potentially had single days (e.g. yesterday) of Covid-19 that caused more damage to human life than (some) whole years of the Flu.

Additionally, there is a high rate of serious organ damage for survivors of covid-19. We don't know how many people will die sooner than normal because of covid-19.

A Texas trauma surgeon says it's rare that X-rays from any of her COVID-19 patients come back without dense scarring. Dr. Brittany Bankhead-Kendall tweeted, "Post-COVID lungs look worse than any type of terrible smoker's lung we've ever seen. And they collapse. And they clot off. And the shortness of breath lingers on... & on... & on."

"Everyone's just so worried about the mortality thing and that's terrible and it's awful," she told CBS Dallas-Fort Worth. "But man, for all the survivors and the people who have tested positive this is — it's going to be a problem."

She says patients who've had COVID-19 symptoms show a severe chest X-ray every time, and those who were asymptomatic show a severe chest X-ray 70% to 80% of the time.

"There are still people who say 'I'm fine. I don't have any issues,' and you pull up their chest X-ray and they absolutely have a bad chest X-ray," she said.

In X-ray photos of a normal lung, a smoker's lung and a COVID-19 lung that Bankhead-Kendall shared with CBS Dallas, the healthy lungs are clean with a lot of black, which is mainly air. In the smoker's lung, white lines are indicative of scarring and congestion, while the COVID lung is filled with white.

"You'll either see a lot of that white, dense scarring or you'll see it throughout the entire lung. Even if you're not feeling problems now, the fact that that's on your chest X-ray — it sure is indicative of you possibly having problems later on," she said.

https://www.cbsnews.com/news/covid-lungs-scarring-smokers-lungs/

I (think) I had Covid-19 back in April, and even though I had a mild case and recovered fine as far as I could tell, I still have weird burning pains in my lungs today. That's a little scary.

Warning graphic image of lung damaged by covid-19.

Spoiler