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COVID-19: The Cold Equations
This is my attempt to explain some of the dilemmas of ‘restart’. It pulls together a string of comments I made on this post. (My thanks to @rodin for not only that post but his whole series tracking the pandemic and its implications.) There will be math, but nothing worse than simple algebra. Estimates are sourced with inline links. Qualifications and elaborations are at the bottom in footnotes. Off we go:
1. There is no pre-existing pool of COVID immunity in the population. There’s a theory that COVID arrived here earlier than officially recognized, and was the cause of some of the nastier upper respiratory ‘flus’ of the mid-winter. This has been pretty thoroughly debunked by testing of patient samples that were preserved from that time. See the Twitter stream here (RTWT) with additional discussion here (post 7/ and onward). The CDC has a standing program to collect samples from ‘influenza like illnesses’, see here and here. This is done for flu vaccine planning and evaluation on an annual basis, and predated COVID. So there’s a large pool of existing samples that would have disclosed any earlier infections.* There’s no magic, we have to go on what’s shown by current testing and cases.
2. The case infection fatality rate in the US is somewhere around .6%
As of this writing, there are 646,300 positive tests in the US, 28,640 deaths.
Assuming a 7/1 ratio of total cases including asymptomatic & minimally symptomatic (nonpresenting) cases to positive tests (based on early Wuhan data) implies 4524100 actual infections.
28640/4524100 ~ .6%
This is probably a bit low, since some currently unresolved cases will end in death.
3. Trying to reach ‘herd immunity’ would be a catastrophe
In its pure form, herd immunity is the idea that an epidemic can be stopped by immunity in the population. The level of immunity required is implied by the R0 ‘R-nought’ characteristic of the infection, which is the average number of persons infected by each current carrier. If R0 is below one, the epidemic will eventually die out. If some of those who would otherwise be infected are already immune, R0 can be effectively reduced. To use a simple example, if the raw R0 is two, then having more than half the population already immune will take it below one. For more discussion, see this paper and this twitter stream. **
The paper linked above contains an estimated R0 for the onset of the US infections of 3.29. This implies a critical herd immunity threshold of about 70%.
My current estimated total cases is 4,524,100. The US Census estimates the current US population at about 329.5 million. So our current case percentage is 1.37%.
To get to pure herd immunity we need 70/1.37 more cases that result in immunity, which is about 51 x.
51 * 28,640 current deaths = 1.46 million deaths to reach herd immunity in the US.
We aren’t going to do this.
4. Antibody tests will not become a ‘pass’ to return to work or socializing
Current case percentage is about 1.4%, see above. Let’s assume we are about halfway through the first wave, which is consistent with the IHME modeling, so we have about 2.8% previously infected and hopefully immune by its end.
You can’t restart an economy with 2.8% of the workers and customers, and no one’s going to put up with rights infringements implied by a pass system to get that level of benefit. ***
Antibody testing will be very useful, but more in finding out what the actual case count has been as opposed to those formally tested positive, which can turn my back of the envelope estimates into hard numbers.
5. Distancing, masking, and isolation will be with us for the duration
R-nought can sound like it’s an immutable constant, but it’s not. It’s an effective rate that is roughly:
(A true constant that is characteristic of the virus) times
(The average number of exposures from each carrier) times
(An average probability of transmission per exposure)
Herd immunity goes after the last term, in a brute force manner, but using it alone is a disaster. Stay-at-home and shutdowns are a brute force way of affecting the second term, but using them alone is an economic disaster.
Masking is an attempt at mitigating the third term – cut down the chance of transmission per contact. Distancing affects both, fewer people encountered and less chance of infection per each. Isolation gets known cases out of circulation.
Unless and until a vaccine is found and distributed, we’re going to be trying to get R-nought below one by a variety of such measures, pushing the virus into small enough populations that it can be traced and victims isolated. Since we don’t have hard data on what measures have what results, the initial response has often been to take it to the limit. Now we have to back off and learn what’s real, what this article calls ‘the Dance’.
If there’s a policy lesson here, it’s that a uniform, nationally mandated response is the wrong approach. This a case where the ‘Laboratory of Democracy’ in the states will be all too real, and necessary to find combinations that work.
* There’s some speculation that a recent heavy case of common cold might confer some resistance, since colds are also caused by coronavirus of a different sort. Any such effect would, however, be incorporated in the existing caseload.
* For those who want more depth on the analysis of the virus’ arrival and variations, see here for an amazing display of what can be done with current RNA sequencing technology.
** For simplicity, this assumes that immunity is an all-or-nothing thing, typically not the case. So it’s going to be an average, not a hard number.
*** To make matters worse, while there are effective antibody tests being produced, we don’t actually know what level (IgG titer) of antibody confers effective immunity. It’s known that asymptomatic or mild cases of COVID-19 produce lower levels of antibody, whether that creates immunity is also unknown. We’re going to be figuring this out on the fly.
As I understand it, work was being done for SARS and for MERS vaccines when they stopped being a problem here. Funding dried up and the researchers moved on. For a hopeful view of our chances, check out this podcast on Ricochet. Of course, no one knows the future.
This is a very important result. I think that this is the key quote from the linked article, quoting a Stanford professor of medicine: “Our findings suggest that there is somewhere between 50- and 80-fold more infections in our county than what’s known by the number of cases than are reported by our department of public health.”
This deserves a separate post. Ontheleftcoast, you should have the honors.
This is more corroboration of a growing trend. I posted on the Gangelt study in Germany, suggesting that there may be 30 times more cases than reported. Recent reports from NYC (pregnant women) and Boston (homeless) suggested similar results — I calculated 20 times from the data on pregnant women in NYC, but I didn’t calculate it for the report out of Boston.
That’s insane. It’s predictable, but idiotic.
Is it accurate to say this is a disruption of supply and demand? I’d go so far as to say it should be illegal for any farm dependent on govermment subsidies.
Even if severe deflation is worse than inflation, surely some natural fluctuation in prices is as integral to healthy markets as allowance for recessions and recoveries. If the oil industry must stomach years of excess supply, why not agriculture?
@arizonapatriot, it’s all yours. I’ve got a backlog of webinars I paid for to do and don’t need any more excuses for procrastination.
Something of the sort is very predictable when multi-stage supply chains are abruptly thrashed as the lock-downs caused. It’s called the ‘bullwhip‘ or the ‘beer game effect‘ after a famous MIT supply chain training simulation. No insanity or idiocy is required, it’s a property of the system. (I’ve played the game twice, both in facilitated face to face sessions with some very senior managers. No, we did not manage to stop the whip. It was a lot funnier the second time since I knew what was coming.)
The most recent criteria that I’ve seen for COVID contact tracing is 10 minutes of contact within six feet to be worth following up. Other estimates are potential contagion within 6 to 14 feet, depending on who you listen to, as a result of droplet spread, hence the recommended social distance. None of those is consistent with the virus traveling all the way through the air circulation system inside a cruise ship and still being viable.
Theoretically safety shouldn’t be a huge issue, at least depending on the platform used.
There are so many types of vaccine platforms nowadays it’s hard to summarize them all. But there are a few that are essentially plug-and-play: an existing vector onto which you “splice” the part of the coronavirus that the immune system is supposed to recognize. The rest of the vector has already been tested in humans over the past decade(s) and has been shown to be safe and efficacious. In these types of situations, safety wouldn’t be the issue as much as a potential lack of efficiency.
But yes, we’d definitely have to test any promising candidate. If it’s an obvious home run the testing phase can be shortened quite a bit (so that it only lasts two months or so).
One real potential dilemma, though, is that in order to test any vaccine, you need to have some reasonably large group of people be exposed to the virus. At the moment, we seem to be in a state of paralysis where we’re afraid to let anyone be exposed to the virus, let alone the thousands or tens of thousands who would require exposure to statistically evaluate the efficacy of a vaccine.
So does that mean the articles I’ve read that blame Norovirus on ships partly on the closed A/C systems are wrong, or is Norovirus different?
Nope, I am just an Ops research analyst with a modicum of modeling experience.
I believe it is possible because these folks think it possible.
SARS-CoV-1 did seem to spread by aerosol.
Remember that this isn’t homogeneously spread.
NYC is going through a streak in which about 1 person out of every 1,000 will die of (apparently) Covid-19. Assuming a relatively moderate infection fatality rate of 0.5% yields about 2 million New Yorkers who are or will soon be seropositive, or about 25% of the city – as a conservative guess. That’s enough to make a difference in the workforce, and also enough to slow the transmission curve noticeably.
There wasn’t hostility to the findings. The criticism was directed at the slapdash way in which the results were presented: at a press conference with absolutely no context. Contrast with the recent roll-out of the Stanford study by Eran Bendavid and Jay Bhattacharya: they went public with their results simultaneously with the online release of the manuscript that shows their work and how they reached their top-line numbers. The Gangelt people couldn’t even clearly say how many people in Gangelt had been diagnosed as positive by PCR (it turns out it was 5% after all, so “only” 3x more people were identified).
Frankly, I would file the Gangelt study in the circular filing cabinet for the moment and focus on the two PCR-based findings (the pregnant women at Columbia and the homeless shelter in Boston) in one category, and the Standford Bendavid study in another.
The PCR-based studies are interesting but not particularly shocking. As I mentioned in my previous comment, we can assume that at least 25% of NYC residents have become infected in the past few weeks just by conservative extrapolation from death figures. So 13% PCR-positive isn’t particularly shocking. Also, when it comes to PCR-diagnosed cases, “nonsymptomatic” can also mean “haven’t gotten symptoms YET”.
In contrast, I think the Bendavid study could be a genuine game changer. Their sample size is much larger than any other serology study to date, and they clearly state their raw numbers (which showed only 1.5% seropositive) and explain how they weighted those raw numbers to get to 2.8-4.5%. They are also more transparent about the sensitivity/specificity of their antibody test. But most importantly, they show a high percentage of undetected cases in a setting that otherwise showed no obvious indications of having a higher case load.
It’s a travesty that this study isn’t already on the top of the website of every major news organization.
It’s theoretically possible since most people have been infected by coronaviruses in the past, and there is some slight antigenic overlap between all of them.
However, when SARS-CoV-2 emerged, quite a few labs pulled out their archived blood samples and tested them against the new virus. This isn’t a 100% airtight method, but generally speaking if there is some degree of pre-existing cross-immunity to a new pathogen, you can identify it in the lab using patient serum samples. But in the case of SARS-CoV-2, these tests all came out negative, suggesting no cross-reactive immunity.
There is a theory that some people who had a viral respiratory infection in their very recent past (or who were vaccinated using the BCG vaccine recently) may have transient protection based mostly on the fact that their immune systems would be in a general state of “high alert”, but this protection – if it existed – would presumably subside fairly rapidly.
I believe Norovirus is different. It used to be called “Legionnaire’s disease” and IIRC it was originally detected after spread through the air conditioning system in a hotel where an American Legion convention was being held. So that virus at least tolerates distribution ‘naked’ in the air pretty well. (I’ll shut up now and let one of the real medical folks chime in.)Retracted. See @mendel ‘s post immediately below.
Legionnaire’s is completely different from norovirus. Legionnaire’s is a bacteria that kills a high percentage of infected people. Norovirus is a virus that typically does not kill, it just makes its sufferers wish they were dead for a few hours.
Legionnaire’s is indeed spread by aerosols (although interestingly not human-to-human, but rather it grows in water supplies like those in an AC system) and is indeed spread through HVAC systems. Norovirus can also be spread by aerosols, but usually not in the same long-distance manner. It’s also not usually aerosolized just from exhaling, but rather is released into the air through vomiting.
Whether SARS-CoV-2 is indeed spread by aerosols still seems up for debate, although even if it can, it doesn’t seem to be able to travel anywhere as far as other classic pathogens spread by airborne transmission.
If we get the testing rolling, lack of homogeneity can be an asset. Do serology on population in areas with large exposures and the law of large numbers works for you. Do the controlled experiments in areas with less exposure where the healthcare system isn’t completely hosed.
I can accept that uncoordinated supply chains suffer from unpredictable variations in stock and service. What strikes me as unethical is the destruction of new and intact goods, presumably to sustain a higher selling price.
Maybe destruction of crops can occasionally be justified in that the costs of storing and transporting excess goods are great enough to negate profits and make the business unsustainable. But anyone who has ever put old furniture out by a street knows that impromptu sharing of excess goods is feasible even those goods are in poor condition. If one makes excess known, interested parties will often acquire it at their own expense.
What needn’t be wasted shouldn’t be wasted. For food especially, that should be obvious.
It’s particularly irksome when government programs, like those under FDR, mandate such destruction and idleness.
But maybe there is something in agriculture akin to flaring of natural gas of which I’m unaware.
The problem with your analysis here is that you assume an infection fatality rate of 0.5%, which is what we’re trying to figure out. I suspect that you’re estimate is pretty good, but what I’d really like to see is solid evidence that would allow us to conclude that the IFR is low. This would put a reasonable upper limit on the number of deaths that we can expect.
I’m going to do a post on the Bendavid/Bhattacharya study — unless you want to do it.
I have thought from the beginning that the lockdown was a big mistake. I must concede that there was considerably more uncertainty about the potential death toll when these decisions were made, about a month ago. I’m actually concerned that President Trump will end up being blamed not for lives lost, but for a rash overreaction that devastated the economy, saved relatively few lives even among those who might have died from COVID-19, and cost more lives than it saved due to the neglect of other medical care alone.
Ivermectin and COVID-19, a preemptive strike:
There are rumblings that ivermectin, a powerful antiparasitic drug, has antiviral activity and may be the next hydroxychloroquine. I hope not, because there are real problems.
It’s not meant for continuous dosing. This is the same stuff that is used for heartworm in dogs. When its used in people, it’s dosed one to four times… a year. I hadn’t progressed beyond “this [expletive] is nasty and they seem to be using a lot of it” and “OK, in vitro.” But Chris Masterjohn brings the heat:
I was intentionally using what I consider to be a “conservatively high” IFR to yield a conservatively low percentage of the population (e.g. of NYC) that is already immune. In my opinion, even that “low” level of approx. 25% is high enough to be of high value.
It’s also worth remembering that since about 0.1% of the total population of NYC seems to have died from Covid-19, an IFR below that becomes implausible at some point. Obviously there are justifiable questions about how many of those deaths can be rightfully attributed to SARS-CoV-2 and whether the population of NYC is representative of the rest of America, but there are also the counterarguments that many deaths in NYC may have gone missing, other regions in the US also have populations that skew old/infirm, and in any case if we expect herd immunity to kick in somewhere around 70% than an absolute fatality rate of 0.1% translates to an IFR of at least 0.14%.
I gave it a shot but if it’s too long and rambling feel free to write something better and I’ll gladly take mine down.
Given what we knew at the time I think it was justifiable, albeit certainly not an open-and-shut case.
Given what we know now I don’t think it’s defensible any longer in most regions of the US or Europe. I do think a structured transition period (with adequate time to gauge the effects of loosening restrictions) is advisable, but we shouldn’t dally.
Frankly, I care much less about Trump’s reputation than whether or not we enter a new depression. That’s not a dig on Trump, but rather: we now have much bigger fish to fry than how history judges any given figure.
The trouble with Ag products is that the spoil rapidly if not processed quickly. Even grains. Meat on the hoof can’t be kept that way for very long (I’ve tried). The only thing I’ve heard that was dumped in any quantity was milk, and you know how long that lasts. At times we made a lot of government cheese to use up and store the milk that the government subsidized the over production of. The problem in the current case is that there weren’t enough jugs to contain what would have gone to the regular channels, and you can’t ask cows to just hold it for a few days or weeks. Since most food products are produced seasonally you can’t turn the spigot back on in a month or two later.
To avoid dumping, we used to periodically create famines in India by dumping wheat on their markets. We drove prices down in India and ruined their farmers, and when prices went up in the US, they had too few indigenous farmers to supply their needs.
What if there weren’t enough orders, coupled with a natural expiration date?
I’ve been thinking more about this.
Unless the virus goes away on its own, everybody is going to be exposed to it at some time. There is no way over a long period of time we can prevent the virus from coming into contact with every person in society. All the “mitigation,” testing, contact tracing, and “social distancing” tactics merely delay when a person comes into contact with the virus. Therefore, aren’t the infection fatalities to get to “herd immunity” inevitable (unless everybody gets a vaccine before herd immunity is achieved, which is suggested not to be a certainty)? The damage from shutting down people’s lives seems a high price to pay when few if any lives will be saved from the virus in the long run.
The shutdown, as you point out, slows the infection to the point where it won’t overwhelm our hospitals all at once. By buying time, it brings a possible vaccine that much closer.
Maybe. We’ve been searching for an HIV vaccine for more than thirty years, and we still don’t have one. We don’t have a cure for AIDS. But what we do have, have had for a quarter century, are antiviral drugs that are effective treatment. That’s why Magic Johnson is still alive. The shutdown buys time for COVID treatment options, more likely than a vaccine to save some lives in 2020.