Keep in mind that "herd immunity" isn't really immunity, it's the point at which Rt (the average number of people each infected person passes the infection on to) drops below 1.0 and the spread shrinks instead of growing. Rt is dependent on how people behave. When behavior changes, Rt can change as well. Each herd immunity level is thus dependent on health measures, which is why "reaching" herd immunity and then loosening up health measures won't work.
Edit: removed wrong information on R0 that's not really essential to my point
I think a big part of the confusion here is how do you clarify the meaning of R0 versus Rt in a context where people don't know the difference, and are using R0 in a context where there is either a time component or obvious public health interventions.
R0 may be a weak theoretical construct, but saying that it's also contextual and not inherent to the virus doesn't do much to clear things up.
Thanks for pointing that out, I corrected the post. It wasn't really important to my point though, which is that we might have enough immunity to let the infections die without football games, while we still have growth with football games.
It would have been more effective if you left it at that. I'm trying very hard to bow out of HN discussions on COVID, you were making a good point in a bad way and it would be a waste to see it lost. Thank you for the correction.
R0 is not a constant inherent to a virus strain. It's a contextual number, determined by population and behavior, population immunity and other factors.
Rt is simply notation of an estimate of R0 at a particular time.
Either way, you're correct that "herd immunity", as used here, means the point at which time the infection rate begins to decline, and this is conditional on population behaviors. If people mix more freely, the estimate changes.
However, the observation that people don't mix uniformly still applies, even if they mix a bit more than they do now. To put it in a CS context, it's like debating the magnitude of the constant, when the algorithm has a fundamentally different asymptotic behavior.
> R0 is not a constant inherent to a virus strain. It's a contextual number, determined by population and behavior, population immunity and other factors.
From Wikipedia: In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted {\displaystyle R_{0}}R_{0} (pronounced R nought or R zero),[20] of an infection can be thought of as the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection.
Population immunity has to be on the list: if the population has some level of immunity, it affects the observed R0. And we can't really measure immunity, other than in very crude ways (i.e. antibody tests for specific epitopes), so we can't control for it.
> Each herd immunity level is thus dependent on health measures, which is why "reaching" herd immunity and then loosening up health measures won't work.
It doesn't apply to non-humans because herd immunity is not something that is at all related to non-human populations. The term was coined to describe a trait of human populations and was found to be difficult if not impossible to achieve in humans until we started to vaccinate.
When cows get mad cow, you quarantine and then kill potentially infected cows. Wild horses have behaviors. They may not change their behaviors when they find a virus, but that doesn't mean that the reproductive rate is independent of the horses behaviors. It absolutely still is.
I appreciate this paper because I feel like every single article about "herd immunity" completely misses the mark and makes some rather poor assumptions. These assumptions are likely made because they make COVID seem like a bigger deal which sells more papers and gets more clicks.
When an article discussing herd immunity assumes a completely homogeneous population I just shake my head and wonder how in the world this article got published.
Whatever happened to large-scale antibody testing? You'd think that someone would be testing a few thousand random people each week to see how many people have been infected to date. That sort of thing was being done in the US back in April.[1][2] But it seems to have stopped.
If you're going to talk about "herd immunity", you need that info to get anywhere.
The antibody tests seemed to be consistently underestimating other measures of Covid-19 immunity, even conservative ones, so they're not considered as useful as we thought in April or May.
It's possible the tests aren't sensitive enough, or immunity is largely based on T-cells (more expensive to test for) rather than antibodies [0], or antibodies for other coronaviruses confer some level of immunity, or something else we still don't understand.
TLDR: "During the first wave of the COVID-19 pandemic, fewer than 10% of the US adult population formed antibodies against SARS-CoV-2, and fewer than 10% of those with antibodies were diagnosed."
The trends won't really tell you much as we get further into the pandemic. Just because someone lacks a detectible level of antibodies doesn't necessarily mean they are susceptible.
Unfortunately, even antibody testing is unreliable now because of waning antibodies.
(One might object and say that if someone has little to no levels of antibodies they must not be immune anymore, but immunity is complex and not solely determined by antibodies)
These models are fundamentally flawed in that they assume immunity or susceptibility are binary conditions. Based on recent research it appears a significant fraction of the population has at least limited immunity from prior exposure to other coronaviruses. They can still get infected but the immune system clears it more quickly and they tend to suffer fewer symptoms compared to immunologically naive patients.
Every model is wrong, some models are useful. Does this flaw make this model useless? On the flip side is it a useful approximation even if it's not completely accurate?
In general, that's one of those anomalous diffusion problems. Unfortunately, there are too many parameters to estimate without simplifying the model. So the reasonable solution is to take a maximum expected value of each and you can still be wrong.
Important data we do not know is chiefly how effective SARS aerosols are and at what range and time.
Well 20% of NYC had COVID and we are currently seeing outbreaks in communities that have relaxed social distancing measures, so it seems obvious that her calculations are incorrect.
That’s part of the thesis of the article. Some populations mix more than others. In the mixing populations the threshold will be higher. In populations with limited mixing, lower.
20% of NYC can have the virus and the general level for herd immunity can still be what is postulated. NYC is incredibly dense compared to the rest of the USA and as such will naturally have more mixing and a higher threshold than say Topeka, Kansas
I really struggle reading academic studies still...
"Heterogeneity in contact structure and individual variation in infectivity, susceptibility, and resistance are key factors that reduce the disease-induced herd immunity levels to 34.2-47.5% in our models."
I THINK that means, in addition to how infectious COVID is, and how susceptible and resistant people are in general, one of the other things that impact herd immunity is "contact structure" and it tends to be sort of limited. There seems to be plenty of "Heterogeneity in contact structure" studies done on many other things out there, so it looks like this is something that's already understood. If I understand it correctly, it means that most people have limited contacts, and while we all might be "6 degrees" from everyone else, we're not directly contacting all those people, and so that could help with herd immunity. So that maybe reduces the number from 74% to this 34-47% number, which better.
Does that mean "Heterogeneity in contact structure" is different for people based on things like how often we go out, where we go, how we travel and where we live? e.g. a subway/bus trip in Manhattan, NY is different than driving alone in Manhattan, KS.
Yeah, that's what it's referring to. People with more points of contact are both more likely to catch the virus and have a larger impact on herd immunity once they're immune.
An example of applying such a concept: vaccinating healthcare workers ahead of otherwise isolated people.
I presume many healthcare workers see orders of magnitude more people per day than average and those people are more likely to be sick (else why are they getting healthcare?) .
Tests this year on blood from people who had SARS in 2003, indicated that 17 years later they still had T-cell responses . On the other hand, coronaviruses which are experienced as "colds" apparently have a lot less retention of immune system recognition. Optimistic scenario is that the immune system is "smart" enough to recognize which infections are a big deal which must be remembered forever, and which are not. Pessimistic scenario is we got lucky with SARS, and may not with Covid-19.
Immunity isn't a binary condition which lasts for a certain length of time and then stops. It exists on a spectrum. The best evidence we have indicates that most recovered patients will retain a significant level of immunity for at least several years.
So, according to this paper 34.2-47.5% of US citizens need immunity before the pandemic can be declared over? So best case scenario we can achieve herd immunity with roughly 100M infections/recovered. USA is currently at ~8M infections/recovered, so that means we are roughly 8% of the way to herd immunity (best case).
At the current rate of +50K infections per day, that's 20 days per 1M infections, so we need 20 days * 92 = 5 years before we achieve herd immunity (best case, assuming no vaccines)? That doesn't seem right.
Well, we could get to 2MM faster if we opened everything up for the less-vulnerable populations (i.e. everyone under 50 without obesity or heart conditions) for whom the survival rate is above 99.99%. You might then be looking at 500k a day rather than 50k.
That is a good strategy. Unfortunately, ppl with survival rate above 99.99% might live with more vulnerable population. It'll be difficult to figure out how to effectively quarantine the more vulnerable population away from the less-vulnerable.
Why not allow healthy people to inoculate with a reasonable dose of the virus so they can control the timing, and then self-quarantine? I would have done that months ago if it was allowed. Even if it only has a partial chance of conferring immunity, doing that would have helped fewer vulnerable people get sick, but instead public health authorities are still clinging to “informed consent” nonsense, as if turning the world upside-down isn’t another serious risk to mitigate.
I cannot fathom how your link could possibly support your contention that 0-4 and 5-17 are "definitely" a 99.99% survival rate (IFR of 0.01% or 1 fatality out of every 10,000 infections). I suspect you are misreading the table? Care to elaborate?
Are you seriously suggesting we lock over 110,000,000 people (34% of the population) in close quarantine for the duration? How do you plan to feed them? Get them medical care (be sure you don't overwhelm the system with the under 50s that get sick)? Keep them from rioting against their captors?
What happens when you decide it's good enough and release them, and the residual infection sweeps through that population like wildfire?
>Are you seriously suggesting we lock over 110,000,000 people (34% of the population) in close quarantine for the duration?
As opposed to 100% of the population? It sounds like an improvement to me. I'm suggesting relaxing restrictions for a part of the population, not increasing them.
If you think 100% of the population of the United States is in quarantine now, I suggest you check the definition of quarantine.
If you relax "restrictions" on a part of the population, more of that population becomes infected. If you do not increase the restrictions on the remainder of the population, the higher prevalence increases the transmission rate in that remainder. And thus deaths.
You would have to increase restrictions for the vulnerable group because if you allow them to mix at all (even at today's levels) with the "free spreading" group they are going to have much worse odds than they do today. Since you're intentionally trying to increase the proportion of sick people in the less-vulnerable group. People like the "grandma living with family with school age children" or the "30 year old immunocompromised cancer patient with a roommate" get fucked if all those people around them (and around them, etc) simply go back to normal and you don't more actively isolate them.
This might not be a terrible idea, though, if compared to a several-year-extension of what we have now... because over time, the cumulative probably of exposure for the vulnerable will just keep rising and rising if we stay at something like the status quo.
But... that's where things like vaccine and treatment development come in. If a vaccine makes catching it much less likely in 6 months, or treatment improvements make it much less deadly even for the vulnerable in six months, then it's worth spending another 6 months in the current situation.
No one is seriously suggesting we forcibly lock vulnerable people in close quarantine. Instead we should provide those at greatest risk with free hotel rooms if they want to quarantine on a voluntary basis.
Wired? Seriously? I don’t even trust them for tech news.
Here are the authors. They are well credentialed
Dr. Martin Kulldorff, professor of medicine at Harvard University, a biostatistician, and epidemiologist with expertise in detecting and monitoring of infectious disease outbreaks and vaccine safety evaluations.
Dr. Sunetra Gupta, professor at Oxford University, an epidemiologist with expertise in immunology, vaccine development, and mathematical modeling of infectious diseases.
Dr. Jay Bhattacharya, professor at Stanford University Medical School, a physician, epidemiologist, health economist, and public health policy expert focusing on infectious diseases and vulnerable populations.
And I'm sure at some point one of them is going to publish an epidemiological model in support of their position, and not a press release. Until then, they're not even at Wired's level.
I thought I remembered reading early on that icelandic testing was showing that 50% of all people infected there showed no symptoms. Then add on how many people show symptoms but its not severe enough to get tested.
> Then add on how many people show symptoms but its not severe enough to get tested.
Earlier this week we took my son in because:
1. Our neighbors have recently recovered from Coronavirus
2. Our son had a cold / fever around the same time lasting several days
3. He had several days of diarrhea after the cold symptoms subsided
I talked to my coworker whose wife is a doctor and he relayed the symptoms to her and she said it very well could be a mild coronavirus infection.
We weren't concerned for his health because he's handled it just fine, but we figured it would be good to know in terms of avoiding spreading it to other people.
So we called and set up an appointment. They got us in like an hour and half after we called.
Got there and the doctor said, "Nope, no need for a test."
At this point I'm extremely skeptical that the number counts are in any way accurate. Also I've lost faith in the "we're not doing enough testing" argument since we went and tried to get tested and they turned us away.
> Also I've lost faith in the "we're not doing enough testing" argument since we went and tried to get tested and they turned us away.
That does not imply that there is enough testing. That just implies that your doctor or health care system is unwilling to test someone in your circumstances. "Not doing enough testing" is not referring to just test kids not being available, it is also referring to health system policies and willingness/unwilingness to test people.
Well, then add on the number of people who just don't get a test regardless. My child had a fever a few weeks ago, it was an ORDEAL finding a place to get him tested. You have to be quite motivated.
If you're not sick enough to require hospitalization, and especially if you're un-insured and poor and don't want to pay a couple-hundred bucks out of pocket, then you'll probably just ride it out and never get tested. I'm sure this is the state of things for tens of millions of Americans.
>My child had a fever a few weeks ago, it was an ORDEAL finding a place to get him tested. You have to be quite motivated.
That's because the test won't change anything. If it's positive, they'll tell you to isolate your kid. If it's negative, there's a high enough false negative rate that you'll still need to basically treat them like they have COVID (stay home and isolate).
Incorrect. Not being treated early is likely a main factor between likelihood of medium to severe.vs no to mild symptoms, beyond immunity. And isolation of sick patient from viral reservoir (such as fomites and other asymptomatic sick) is known to be important too, as it changes the viral inoculum dose.
Based on New York seropositivity, there would be a 5-6X multiplier on cases I believe. However that could change since they were test constrained when generating lots of those cases (downward?), and demographics of infected have changed (upward? younger may push multiplier higher as they are more asymptomatic and potentially get tested less).
CONFIRMED cases. The total number of cases is probably 5-10x that.
I live in the Deep South, and honestly I suspect that our curves have fallen simply due to a "limited" herd immunity effect (i.e. the groups of people most likely to catch COVID have already done so in large enough numbers). I certainly haven't observed any significant change in behaviors since the July peak, yet the numbers are falling like a rock regardless.
Deaths are probably more instructive – just to get a ballpark number. If only because deaths are less likely to overlook too many people.
If the IFR is around 1% we would expect around 1,000,000 deaths if one third of Americans have to be infected for herd immunity. So that would suggest the US is 20 percent of the way there.
Given the haphazard way of calculating these numbers I would, however, put huge error bars around some (something like ±15 percentage points at least).
I agree strongly with this type of analysis. The data we're seeing is strongly skewed by all kinds of biases. Looking at deaths at least removes one big piece of bias.
I too suspect areas are achieving some limited herd immunity. I don't think the behavioral changes adopted in the US have done much. Mostly, I just think less social people aren't getting it. More social people are.
I have a hunch that in reality the south has had flattening curves because the super hot summer weather is over and people are no longer spending most of their days in air conditioned buildings and are spending more time outside.
And the opposite is now happening in the north (again). People come inside as the weather gets colder, and respiratory infections in general get far worse.
> I certainly haven't observed any significant change in behaviors since the July peak, yet the numbers are falling like a rock regardless.
Picking FL as an example: deaths are down only about 50% since the peak in August (7-day averaged), and the numbers are surprisingly "sticky" (in the sense that they're not going down all that quickly.) For the record, FL lost 139 people yesterday; that's nearly the capacity of a 737.
139 deaths were reported; those deaths actually occurred over the last several months. Which means we won't know how many actually died yesterday for a while, but it's likely well below 139. Jennifer Cabrera posts regular updates with dates of deaths, e.g. https://twitter.com/jhaskinscabrera/status/13139124858340884...
You make this out like I've picked on some rare outlier day, but the state has had multiple days in the past two weeks with even bigger death numbers. The 7-day average is a pretty substantial 85. If your point is that the drop since August has been more substantial, then I would need to know that the older, higher numbers were not also subject to the same delays.
You make this out like I've picked on some rare outlier day
Sorry, I didn't mean to convey that impression. Florida has been regularly reporting daily death counts that include deaths from several months ago.
I would need to know that the older, higher numbers were not also subject to the same delays.
They were, in the other direction. If you look at the date-of-death chart in the thread I linked, you'll see that for a few weeks there were consistently over 200 actual deaths per day, while the reported 7-day average in your chart never reached 200. The delay means that the reported count will be lower than the actual count when deaths are rising, and higher than the actual count when deaths are falling.
And of course we can't be sure which of those categories we're in at any particular point in time; if deaths do start to increase again, it may not be noticeable in the reported numbers for several days. But based on the hospitalization trend I believe it's probable that the current reported numbers overstate the actual deaths.
We know that coronaplague spreads through superspreading events, person-to-person transmission is wildly variable, most people don't infect anyone, but some give it to a dozen.
You'd like to know if people are wearing masks at church or if family get-togethers are now outdoors.
I think the common perception on HN, Reddit, etc is that COVID spread in the U.S. is primary a matter of conservative people flouting its seriousness. I understand the satisfying appeal of that picture.
However, I'm looking at my local health department's ZIP-code-by-ZIP-code infection map of the metro area. And it seems almost entirely correlated with poverty, not privilege. Infection spread seems mostly due to "essential" workers continuing to work. That's a problematic thing to point out, because I don't think we can or will solve for that. But it's plain as day.
I think the reason that HN, Reddit et al. have this impression is that state policies in conservative states are explicitly less restrictive than those in less conservative states. Florida just removed all stadium event attendance limits, for example. Within any given state there are all kinds of political beliefs and economic situations that may be more or less correlated with spread, but state governance is a very big variable.
Anecdotally, out here in the rural wilds of Alabama, most people seem to be wearing masks. I recently went into downtown Huntsville and no one was. Poverty and essential workers may be a significant component, but given the behavior of the young and affluent here, I don't think that is all of it.
Yes, you'd say that the Red areas are on aggregate older, poorer and less likely to work from home.
That said, at my regional college in the Deep South, case numbers have dropped noticeably since the beginning of term - instead of 30 cases every day we have now ten, and there have been remarkably few outbreaks at frathouses, all that despite no organized testing.
Conservative people are much more likely to live in rural areas. Liberals in more urban areas. Viruses spread much more effectively in higher population densities.
So you'd really need to look at per capita infection rates and control for density, not absolute numbers.
For some anecdata, in my moderate county we have a mask mandate. The surrounding less populated and much more conservative areas don't. Since the mask mandate was put in place more than half of the cases in my county's hospitals have been from the surrounding counties. Despite that fact that they have an order of magnitude fewer people, and despite that fact that we have far more people living in poverty in absolute terms than they do.
This also assumes that acquired immunity from an infection is complete and permanent. Immunity to other coronaviruses decays over a year or two -- meaning that before the five years are up in your scenario, there would be a significant cohort of prior victims open to reinfection.
So, maybe that means by slowing the infection, what we're really doing is ensuring a neverending slow wave of infections ... forever? Maybe what normally happens with these kinds of viruses is they infect everyone then die out? And if you slow that, they never die out?
No, it means that the expectation that "herd immunity" will be naturally reached, without an effective vaccine, is a pipe dream. Before vaccines, no population ever reached "natural herd immunity" for polio, which has similar R values; you need effective vaccines, effectively delivered, to get that result.
No, we are undercounting the number of people who have it (asymptomatic or not) by a huge factor. at one point it was by a factor of 10, but I doubt that is still the case.
This is why I watch florida like an eagle, because if it stops going up there we know we got a very good estimate to know when the top is.
~2.5-3% (730k/21.5m) of Florida has had it and it's slowed dramatically (use to be like 16k/day now down to 3). It feels reasonable that herd immunity starts slowing down the virus pretty fast somewhere around 25-30%. It seems reasonable it may come to a complete halt by 47%.
This is fag packet math, so I'll spare any exact figures.
But if the second wave data for the UK is anything to go by, confirmed cases vs actual cases was at _least_ 5x for the first wave.
There obivously are other factors, but with increased testing that multiplier only climbs, bringing herd immunity numbers actually within reasonable grasp.
I strongly suspect there have been similar effects in the US.
FWIW they almost certainly didn't write on a cigarette package in this instance ;o)
It's just the name of that type of maths because people used to use whatever small, available, piece of paper was around - so cigarette packs some time ago (you definitely could write on them with a ballpoint pen (ie un bic).
Getting tangential, napkins to me in the UK have always been cloth, and we have serviettes (a French word, meaning sheet IIRC) made of paper to wipe our mouths with.
Our language gets more and more influenced by USA "English" usage, so perhaps youth would just call it a napkin. People do say 'paper napkin' but without the qualifier it's a fancy piece of cloth [to me].
I can't decide whether to use the term cutlery (mainly UK) or silverware (mainly US). They're both inaccurate, especially when asking for plastic/disposable versions.
If it includes a knife then "cutlery" seems accurate? Sometimes I'll just make a compound of the items "spoons-and-forks" (when it's pasta for tea [tea meaning evening meal where I come from]).
> At the current rate of +50K infections per day, that's 20 days per 1M infections, so we need 20 days * 92 = 5 years before we achieve herd immunity (best case, assuming no vaccines)? That doesn't seem right.
I can't remember exactly where I heard it, but I believe robust herd immunity in human populations has never been achieved for a virus like this without the widespread use of a vaccine. Which makes sense, because there's evolutionary pressure on viruses to adapt, and so many diseases remained endemic and common until vaccines where introduced for them.
Edit: in response to the dead reply: the Spanish Flu didn't disappear. It killed tens of millions (out of a much smaller world population) and persisted for decades as a seasonal flu. IIRC, it didn't get eclipsed by other strains until the 50s.
I wonder if this also means that only 35% of us need a vaccination to declare it over. I had previously read 60-70% were needed and that 35% of Americans get a flu shot. That depressed me.
EDIT: seriously, downvoting this comment? Can't imagine why and would like to know.
I don't understand why more people do not get flu shots, unless they have no medical insurance and cannot afford the cost.
It's not always effective, because they have to predict when they make it what strains of flu will be prevalent in the next flu season, and they don't always get that right, but in that case you are no worse off than if you had not gotten the vaccine. But when they do get it right, it can save you from getting the flu. That's certainly worth a few minutes getting it an a couple days with a sore arm.
With a COVID vaccine, I doubt it will get anywhere near the same fraction of takers as the flu vaccine.
1. The anti-vaccine crowd probably won't take it.
2. The "COVID is no worse than a mild flu" crowd probably won't take it. Even if they do, it won't be at a higher rate than they take the flu vaccine.
3. The "COVID is a hoax" crowd probably won't take it.
4. A lot of the people who believe COVID is real and serious will probably be turned off if the approval seems to have involved politicians forcing approval over the objection of scientists who say it is not ready yet. (Especially if those politicians have also been pushing the "no worse than a mild flu" narrative).
> With a COVID vaccine, I doubt it will get anywhere near the same fraction of takers as the flu vaccine.
It will if closures are lifted but vaccination is made a requirement (either privately or by government mandate) for on-site work, schooling, etc. The flu vaccine is treated as primarily a personal preventive medical treatment; while it is encouraged for public as well as personal health reasons, there is no force put behind it. But it is quite possible, and there is plenty of precedent for, public health measures to be mandated (especially a conditional mandate, like for schools, work in particular conditions--including any public content or even on-premises work) and enforced.
45 states allow skipping their conditional mandate for schools if the parents cite religious objections. I expect their COVID mandates will have similar exceptions.
The vaccine won't be 100% effective. The FDA just approves vaccines that are at least 50% effective, and with the margin of error it's possible that they will work in 30% of the population.
The implication here is that having "tested positive" is equivalent to having an "infection". An infection, by definition, is an alteration of the biological state of the entity with observable side-effects (symptoms). It is patently false to assert that "testing positive" for this virus is 100% indicative of an "infection".
Further, "100M infections/recovered" implies that this infection can lead to "recovered" implying that the other alternative to recovere is a terminal/chronic condition. I guess this makes sense if we agree that many millions of "infected" immediately "recover" after testing positive, given that a substantial subset of those who "test positive" are "asymptomatic", reasonably understood as not-ill, not-sick, not-infected. Thus insta "recovery".
My overall point here is that the permitted vocabulary of speaking and reasoning about this phenomena is inexplicably illiterate. Whether this permitted simplistic vocabulary of discourse is by design or a symptomatic of the state of humanity, the inevitable consequence is a degradation of analysis and sub-optimal solutions.
Edit: removed wrong information on R0 that's not really essential to my point