The tricky math of Covid-19 herd immunity
quantamagazine.org
quantamagazine.org
Infections seem to happen at large gatherings: one person can be identified as infecting 50 others simultaneously, especially in the early cases, even though the R-nought is said to be no more than 2.5
That suggests infectiousness is an incredibly skewed distribution, to the point of implausibility.
An epidemiologist apparently setting out R-nought as the underlying basis for their modelling (or even: communicating it to the public as such) worries me.
I wouldn't begin any statistical modelling unless I was thinking about the distribution of infectiousness more generally: even a high school student of statistics would know to look beyond the mean and to the variance.
Even after we drive the "R-nought" low enough that just means that on the whole the fire is 'contained' and will eventually burn out. To achieve actual eradication, which is what is required for something like this disease, a strong concerted effort to isolate and contain is required.
I am also somewhat fearful that there will be a rush towards large events and other high-risk activities that allow these 1 to 50+ mega-exposures from prolific infecters to happen.
One of the core point of the linked article is that R0 has a wide range and therefore can’t be used to draw firm conclusions about herd immunity.
> even a high school student of statistics would know to look beyond the mean and to the variance.
I’m not sure if you’re responding to the linked article, but the article does a good job of emphasizing exactly that point. The R0 and her immunity calculations aren’t strict values or hard cutoffs. They are very situation dependent and will change over time depending on circumstances and behavior.
It’s also important to keep in mind that the current average R0 numbers are measured during the middle of widespread social distancing and similar countermeasures. If people start reducing their precautions under the assumption that herd immunity will protect them, the infection rate might increase again.
Governments don't (or shouldn't) quote it, because it tells you more about the richest person than it does about the population as an aggregate measure.
Epidemics are by definition aggregate effects. They're defined by statistical models at all levels. Everyone involved understands that there is variance in individual cases. That's literally the whole point of the field inventing terms like R0!
I genuinely don't understand what you're trying to say here. It sounds suspiciously like "I don't understand statistics so I refuse to believe in any models that use them."
I do understand statistics and therefore the mean is something I would not use in my modelling when there is a high skew in the data: here, the skew appears to be incredibly high - so the mean (here called "R0") is not reliable at all.
The thing that bugs me about covid-19 is how we only try to optimize for reducing deaths of that one thing (covid-19), while letting other types of collateral damage resulting from said optimizations pile up unaccounted for as side effects. Experts are clearly very bad at predicting second and third order side effects resulting from covid-19 death reduction optimization.
To use a computer analogy, it's like going to extreme measures to refactor all programs so that Covid19Exception kills as few processes as possible, meanwhile processes left and right are dying at elevated rates due to HeartExceptions and BrainExceptions (and in a few months CancerExceptions) and the OOM Killer is on the prowl but nobody is noticing because they are hyperfocused on Covid19Exceptions.
There are two big elephants in the room to consider:
1. Ongoing health effects from Covid. Hopefully not as bad, expensive, and detrimental as polio.
2. Chance for negative mutation.
These two items alone add a lot of economic uncertainty.
[0] https://www.vox.com/2020/5/29/21274416/household-income-surg...
Well, how long will it take to reach 60% with/without heavy preventative measures? If SIP/masks/social distancing drag out the timeline so it takes 5 years to reach herd immunity... you'll have a mental health crisis of the millennium to deal with in addition to covid-19.
I know that the US has one of the higher per-capita infection rates (though not the highest in the world), but we’re not even close to herd immunity.
Less than 1% of the US population is confirmed to have contracted the virus, while even generous herd immunity estimates require 60% of the population to have developed immunity.
The second half of the article purportedly being discussed claims that because of the variability of R0, the herd immunity threshold might be much lower than this. For example, "The paper’s 10 authors, who include Gomes and Langwig, estimate that the threshold for naturally acquired herd immunity to COVID-19 could be as low as 20% of the population." Are you taking this into account when you claim that a 60% threshold is "generous"?
CDC estimates based on seroprevalence data that for every case reported there are actually 10 other infections: https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/comm...
It currently estimates that so far, 6.2% of the US population has cumulatively been infected, and 0.82% are actively infected/infectious today.
But it does vary widely geographically (and likely socioeconomically).
COVID can easily overwhelm the hospital system all by itself. We saw that in Italy and China... and hospital systems in several parts of the US are already near capacity. Once they're overwhelmed, there will be no room left in the hospitals, and they'll have to do one of two things: Start sending covid patients home, which will increase the covid death rate and/or start refusing patients with other injuries/diseases.. which will increase the deaths in those cases.
The restrictions are all about preventing the hospitals from being overwhelmed, and causing more people to die than currently. It just seems like they're so focused on covid, because it spreads so rapidly that it can overwhelm hospitals in a very short period of time.
Unfortunately with the numbers in Texas, Florida, and elsewhere... and with how long it takes for restrictions to have an effect... it's very likely we'll see what an overwhelmed hospital system looks like very soon.
1. Is there anything a hospital can actually do to save someone with a serious case of covid-19? As far as I know, ventilators are ineffective (and may even make things worse?). If 100 people with serious covid-19 are taking up ICU beds, how many will live due to direct hospital intervention? If it's a very low %, it seems like a no-brainer to turn away covid-19 cases in favor or other, more treatable diseases. Otherwise it's like letting people with prion disease use up all the ICU beds despite their condition being pretty much untreatable.
2. Anti-covid measures can do the inverse. Remember back in March/April/May when all the hospitals in the USA were empty due to SIP? Most hospitals ended up dismantling their temporary covid-19 field hospitals due to lack of use.
New treatments are being developed every day, so those numbers may get better.
2. IMO, dismantling the field hospitals was a terrible idea. They built them early, locked down, then saw the decline and people started thinking we were going to eradicate it like in New Zealand. It was never going to happen.
Also remember, doctors and nurses are people, too. Who is going to save your ass if all staff is sick?
A hospital wouldn't be turning them away, they'd be throwing them out. Any likely fatal case of covid is already in the hospital.
That's death panels on steroids.
What survival percentage should get people ejected? 10%? What would be the social consequences of turning people away from a hospital who would live 10% of the time? Should they also start turning down people in serious car accidents or who have had serious heart attacks? Where would these triaged be sent? Would there be some sort of lightly manned hospice warehouse where suffering people wait to die, or would it be more merciful to give them an injection?
If you don't give them an injection, but 1-2% of the time they still end up recovering on their own, how would we answer them when they start loudly and publicly asking questions about our priorities?
These probably aren't questions that you would personally have to answer, because your role in this hypothetical is just to not be on lockdown and to be free to do whatever you want when you want, but other people are going to be required to physically carry this stuff out.
> Most hospitals ended up dismantling their temporary covid-19 field hospitals due to lack of use.
This is good news, not bad news.
[1] There's plenty of data on economy vs health from the circa 2008 economic implosion. We could start with that, but we haven't. That's risky, for some fatal.
We'd also need to account for a drop in deaths from fewer car and workplace accidents.
It’s true that bad government responses can exacerbate things (as the US seems intent on proving), but the pandemic was going to inflict serious economic damage anywhere it reached the uncontrolled state like now exists in the US.
The only way to have prevented that was to act early and competently, which many countries have successfully done. But once you’ve crossed that threshold, demanding people risk serious illness and death for the sake of the economy isn’t going to get you very far in correcting things.
Why are we assuming? What if the path we're on is worse? Do we really expect the elected officials to admit the error? Will the media ask?
It's wrong to assume. If nothing else it devalues the lives lost and damaged from the side effects. Either we're all in this together or we're not.
We know what kind of responses are effective and limit economic damage and death (Taiwan, South Korea, and Vietnam) and those that do not (the US, Sweden, and Brazil). Again, the economic impact and failure to confront the disease are inextricably linked. If you’re argument is that “if we’re already doing poorly, why do anything?” then the answer is the depth of how poorly we’ll do depends on what steps we take to mitigate the damage, even assuming we’re already on a bad path. It’s the difference between causing hundreds of thousands of deaths because of our screw up vs millions.
All of this bad response spectrum will also have varying degrees of terrible knock-on effects, but those also exist because of the failure to intervene early and effectively, and put the US on a good path.
That's it.
The US is probably in for a lot of pain because it refuses to acknowledge that throwing more bodies at the economy, irregardless of safety or sanity, isn’t going to fix things.
If we can model the virus' spread and buy into that interpretation, why can't we also try to model and discuss the "side effects" of that "war"?
Also, while they loudly talked about risks, they were not saying we should not do lockdown. Turns out, abused people get sick too and can get their relatives sick too.
It's a massive mistake to assume the total collateral damage is minimal.
How are they completely unaddressed? The varying state responses and reopening strategies show that they are being addressed, just with different priorities. Some states have heavily favored shutdowns to minimize the direct impact, while others have weighed the second order effects as more critical and pushed to reopen more aggressively.
- deaths due to an economic collapse
- the longer term affect on health outcomes due to the economic collapse
- suffering and deaths due to delayed health care
- increase in deaths due to suicide
- increase in suffering and deaths due to substance abuse
- suffering and deaths due to domestic violence
- Increase in obesity and diseases related to lockdown
- And so on...
- And so forth...
There's an unsubstantiated narrative that dictates that Covid 19 is public enemy #1. The disconnect is that narrative is in truth a balloon grab. There _are_ plenty of negative and deadly side effects from blindly embracing that narrative.
This isn't about Covid 19 being real. It's a headon realization that the aggregate side effects of "going to war" with Covid 19 is producing significant collateral damage. Assuming the former is more significant than the latter is naive and negligence.
That is not to say that we shouldn't take measures. What it's saying is that the measures in place are not doing well at accounting for all impacts, which is certainly a difficult problem.
What I can tell you is this: I happen to have first hand experience from a country that initially took some of the most draconian of measures when the virus surfaced. All with the usual explanations as for why all that was absolutely necessary.
Then, after some time, the local ruler needed to secure a reelection he had already planned before the virus spread. All of a sudden, it was like there was no virus anymore. Of course there was, but the topic was practically taboo while the elections where going on. Now that the elections are over, and said ruler has galvanized his position for the foreseeable future, the virus has returned and the number of infections grown. No surprise that stronger measures came back too. But that's not the interesting part.
What is interesting, is that during the elections none of the doom scenarios that almost every country around the globe has used to justify/explain their measures (whatever those might be), happened. There is a good chance that a lot of bad news was suppressed and covered up. If only to ensure the election would not be forcefully shut down. But there are only so many mysteriously dead people and failing hospitals that even a government with absolute power and no accountability can cover up.
The point here is this: that despite all the rhetoric about why all those draconian measure were so much necessary, when they were (practically all) temporarily lifted for political reasons, the world did not stop turning and neither did any systems collapse. In fact, in many/most aspects the country managed to temporarily recover more/faster than other countries in the region. That was, of course, until the election was over, and the virus "returned".
I am not saying that any of the measures are wrong or that they didn't help prevent deaths. But what I am saying is that maybe the "reasoning" regarding what will happen without them isn't as much established fact as many people like to believe.
Either way, it doesn't take rocket science to figure out which country I'm speaking of.
I "only" suggested to be careful about assuming what will happen to the systems, when the current measures are (temporarily) gone. That on itself should not be a revolutionary act in the first place. Remember, assumptions are the mother of all fuck-ups.
If I did not have a seriously surprising experience myself, regarding the story I told, then I certainly would not have responded as I did. But decide for yourself what you do with the info. If you (want to) dismiss it all outright, only because it does not come in a package you demand, then go ahead. I honestly couldn't care.
If you had perfect quarantine for a month, you would eradicate the virus. If you had harsh measures for a period of time, then ended them in order to do some massive social event, I'm not sure why you would expect outcomes similar to if you had never had a lockdown. A harsh quarantine is a reset button. Places need a little time and a few outsiders in order to be reinfected and start the process again.
And of course if the initial lockdown measures were effective, the base for a new wave of infections would be low, and it would take a separate 4 to 6 weeks for the next wave of cases to become seriously problematic.
However, my point was that the lifting of the strict measures did not lead to the collapse of the healthcare system, which was the justification of the initial measures. Consider also that the local healthcare system has been only a vague shadow of the advanced state of those in more "developed" countries.
In a way, what the locals may call a "social experiment", might be one of the few existing empirical test cases for what really happens when measures are (all but) lifted. Arguably it might also be true (although I think to a lesser degree) for some other countries in the region.
With what I know first hand, the virus certainly was not eradicated or conquered before or during the election. But the political response/dealings with that is a whole different discussion, and not one I want to have here.
So after reaching that state, which can be imagined as a "reset", the virus starts to spread more actively again once the measures are lifted, and of course there is a period where nothing "big" is visible. But that is also what we have seen in many European countries at the start of epidemics: the exponential curve has a phase where the number of cases is very low. Only later it gets to be much worse, fast.
The lockdowns work. You‘d have to somehow prove your claim for me to believe you.
I'm not here to debate you (or anyone). I will point it out, when people respond with something that is either incorrect or not applicable, but more out of courtesy than to convince anyone. It's just because they might not know the relevant local situation as I do. But, I sincerely don't care whether I convince you or not. Your mistakes and ignorance are your own responsibility; your funeral. I don't have to show or prove you anything.
I did not say that lockdowns don't work. They certainly did have (some) effect here. On the other hand, the virus did spreading either way, even with some of the most draconian measures taken anywhere. Those were new infections, for months. That in itself might at least suggest that you require extremely disproportionate measures (causing all kinds of damage) to really influence/contain the spread this way. That is, (especially) if you essentially don't test anyone. However, that's a whole different discussion/topic.
What I originally pointed out is that it was odd to see how, when all measures were lifted (for whatever the reason), none of the earlier predicted doom scenarios happened. Which should cause at least pause and wonder (or reassessment) whether those predictions/assumptions are actually accurate in the first place.
You can throw back in a theory, which wasn't applicable in this particular situation, which I can tell from the details/facts I personally know. Then you can throw a tantrum/fit, while claiming to know some unquestionably truthful/factual, and argue that therefore I must be wrong. Well, maybe your own beliefs are still the actual wrong part here.
Mind you, I don't give a shit about any political side or beliefs. Nor was I really bothered with any of the measures (not even the draconian ones, although they should be useful and not just a political tool). However, my big gripe is with people that take what ultimately still are estimations and predictive risk assessments (which in themselves are perfectly okay and reasonable, as long as they get updated with new insights and understandings), and start presenting them as canonical gospel that can not be questioned and should be religiously defended. There should be no place for dogma like that in science (or anywhere, for that matter).
To do science (or even do any conclusion) one needs verifiable facts. It's facts that I miss here. That you claim that somehow you “know” something that doesn’t match any other observation, without providing any numbers or data at all, except hearsay, doesn’t bring anything to anybody. My only conclusion is that your words, unsupported by anything at all, after seeing different behavior across the world for months just can't be trusted. What’s the difference between your claims and any claim appearing on 4chan?
If you would publish your data where it can be verified that it shows something that is completely opposite of what's observed in the rest of the world... that would be something that I would surely praise. And the rest of the world probably too. Imagine that... something that gives a new information different to the experience of the rest of the world, and it is actually true. I just don't see that in your messages.
The dynamics of epidemics are known: Rt > 1 produces exponential growth. But the speed of growth is dependent on the value, and every exponential function has the initial part that "still doesn't look bad." Rt = 1 produces linear growth. Rt < 1 results in the decay of the number of cases. You somehow claim that you see something different than that, even if the simplest explanation is that your hearsay story was based either on Rt > 1 but on the small number of starting cases or on Rt practically being around 1 where the number of new cases is never hard for the health system, or it can be that during the period described Rt oscillated around 1, again not stressing the health system. And all that is dependent on behavior of millions of people, who can in their environments, which could be relatively isolated from the rest, have their own initial conditions and their own Rt values.
But we just don't know what happened there -- we have no useful data from you.
I've checked, there's no point:
It "worked"... but only for a short time! Now the number of reported deaths per day reached the highest since the start of epidemics.
And before that short time of "everything's open", the measures enforced were among the strongest applied in Europe.
So the whole episode doesn't prove anything. Yes, after the extremely strong lockdown a small country can pretend for a month or so that "everything's fine" and that is totally unsurprising: look at the shape of all exponential functions: the start always appears so close to the x axis. Only later the exponential property of the curve becomes obvious, especially knowing that a person infected today won't be immediately sick and even less dead -- it takes time. And the spread continues during the time most have no or mild symptoms. Big countries can do all that even longer before the problems can't be hidden. But sooner or later the need for new hospitals for newly infected patients becomes obvious, which is exactly what can be seen now.
No country is going to bluff its way out of this pandemics. More than one tried.
My favorite country is Vietnam: they still have zero deaths in a country with 100 million inhabitants. Maybe other countries should check what they are doing? Also, Taiwan has only 7 deaths up to now, having 23 million inhabitants. Thailand has only 58 deaths, with 70 million living there. These three countries have together 200 million living there and still less than 100 reported deaths.
Taiwan banned the export of surgical masks and lifted it only a few days ago, and produced even 20 million masks per day(!) for its own needs:
https://www.taiwannews.com.tw/en/news/3959712
Think about it: it produced a new mask for every its citizen every day.
Taiwan had around 20 cases total and exactly one death in the last two months.
I don't think anyone thought of it as established fact. But it also wasn't an established fact that we didn't have to take all those measures. It's a question of risk, not of absolute foreknowledge.
Also, as @acqq correctly points out, a period of time with strict lockdown can reduce the number of cases to the point that a relaxation of controls doesn't immediately result in a large outbreak. An exponential curve has a flat region [0] where it doesn't seem to be getting out of hand. If you manage to put yourselves well into that flat region, you will have bought yourself a period of time in which the controls can be relaxed. But it's only temporary.
income can be replaced, death is ultimate....
Also, we generally know that for every 1% increase in unemployment, there are 5000 extra death a year... (sickness, suicides, lack of basic items etc) so a 10% increase of unemployment, will cause an extra 50k deaths...
Meanwhile covid has already caused 130k+ deaths. If left completely unchecked it can go into millions territory... (1-2 mil).
If you halve the covid deaths, you can save at least 500k lives, at the collateral expense of 50k lives (due to rising unemployment).
A lot of people don't understand that death is a threat until they start to experience a lot of it in their cohort. If that happens after exponential growth, you get a sudden phase change where a large percentage of the working population switches from "This won't touch me and I don't care" to "OMG this is going to kill me."
At that point people stay at home regardless, and the economy is badly damaged anyway. The difference is it's damaged in an uncontrolled way, with panic buying and supply chain interruptions - neither of which you want.
The awful truth is that it's actually better to allow some businesses to die in lockdown as a fire break than to allow a pandemic to get completely out of control - because the latter results in a much higher death toll and more severe economic damage, as well as a permanent loss of trust in effective government.
There’s no evidence to support your claim that unchecked spread of covid would lead to a worse economic disaster than the lockdowns, and in fact Sweden and Belarus seem to directly contradict it.
It's not a choice of doing nothing and having a stable economy at the cost of increased human suffering, it's a choice between severe economic damage because of lockdown measures and severe economic damage because of human suffering, healthcare costs and workforce capability reduction.
Our economy was precarious before covid, and we were granted the perfect excuse to juice the economy. Congress held back (although we did far better than what was done after 2008) and spent more on crony giveaways than high-multiplier direct payments to individuals. The replacement that we did for incomes kept people in quarantine.
Servicing people in quarantine was also an excellent opportunity to expand employment by the state that mostly wasn't taken, except by Amazon and big box stores.
And the roadwork we could have gotten done. That one really annoys me. Outdoor jobs without close contact should have been ramped up. We had perfect weather for it in the US.
A real quarantine would have been legitimately over by now in 99% of the country. I've even read that cities who were good at quarantine didn't even see much of a rise in cases due to the Floyd protests (based on positive test rates in people who said they protested) while places that had looser rules are seeing a bump from the protests. To me, that means that places that instituted complete quarantines were pretty much out of the woods a month ago.
Some good tweet threads on this major point of contention:
https://twitter.com/mattyglesias/status/1277236932121157632 (Carl Bergstrom, in the replies, is one public health figure who insists he originally meant essentially flatten as much as possible).
Nate Silver insists most people understood flatten the curve in March to mean mitigation: https://twitter.com/NateSilver538/status/1277347535061946372
One of the few nations to actually follow the "mitigate Covid to prevent health care system collapse" is Sweden. The fact that the media/experts roundly criticize Sweden for having too many deaths (despite their health system not collapsing) is another piece of evidence that they really mean "flatten as much as possible."
1. It kills people and causes long run harm to many survivors
2. It can also overwhelm health systems, which leads to more deaths than otherwise and prevents the treatment of normal medical problems
You obviously want to avoid #2. But it also makes sense to avoid #1. “Flatten the curve” makes it seem like #1 is not so bad.
I said flatten the curve myself. I meant eliminate both though. It’s not that much more effort, as many countries have shown. In fact with a head start it was much less effort.
We have a harder road ahead now though in places where it is not eliminated.
But I am not sure anyone can find a credible expert who said “flatten the curve and keep letting it run through till a vaccine”.
Countries that locked soon are opening up and then locking parts of activities selectively - but this time with easier and cheaper tests, with everyone having masks and so on. There are proposals about closing and opening schools in two weeks schedules. Economies were open in step by step way.
What makes you think uncontrolled covid will have no negative effect on heart, brain and cancer? If hospitals turn into covid centers you can’t safely treat those high risk groups.
Further, there’s lots of possible long run effects in survivors we don’t know enough about yet. So there is an unbounded downside risk to covid infections.
Finally, we don’t know if immunity persists. We hope it does, but it might not, in which case letting it run through the populace will lead to more deaths when people catch it a second time.
Plenty of countries eliminated it by acting early. The US had that option and discarded it, and now is in a worse situation. Maybe the right approach given this worse position is to charge ahead, but you’re ignoring a lot of second order effects yourself.
This is a common assumption, but I believe it's incorrect. As I showed by analyzing the pandemic as a classical feedback system [1], the long-term policy curve isn't just a simple tradeoff (i.e. "optimizing for reducing deaths of that one thing"), but is actually like an inverted parabola [2] with three regions.
But you are correct that our current public policy (by which I mean aggregate US public behavior, not just official policy) is currently targeting one of the worst long-term outcomes, which includes both higher-than-necessary COVID-19 deaths, AND higher-than-necessary collateral economic and other damage.
I believe that with a different strategy we can probably reduce Covid19Exception and simultaneously reduce HeartException and CancerException.
[1] https://www.circuitlab.com/blog/2020/05/28/surprising-covid-...
[2] https://cdn.circuitlab.com/misc/20200526_SurprisingCOVID19St...
I've also read that in the 1918 Spanish Flu pandemic, the cities with the most stringent lockdowns were the ones whose economies recovered the fastest -- so your model has some empirical support.
The USA literally, literally did the opposite. We tried, in the initial outbreak, in a few areas, to reduce infections to a manageable steady state. It worked.
Then most of the country threw those rules out the window and engaged in some combination of "opening up", relaxed enforcement, and what amounts to a straight up propaganda effort by much of the executive branch and the largest TV news network to convince people that no containment effort was needed.
And.... here we are. Covid is controlled pretty much every except in the USA right now. Our outbreak is as bad as it's ever been.
Citation?