Edit: removed wrong information on R0 that's not really essential to my point
I think you just devalued your argument.
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.
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.
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.
Yep. Here's a very approachable and well written paper on the topic: https://academic.oup.com/cid/article/52/7/911/299077
And my comment on it from 6 months ago: https://news.ycombinator.com/item?id=22818413
This seems like something you made up. Can you cite your source?
How exactly does your rule apply to non-humans? What "health measures" do packs of wild horses take when disease comes to the herd?
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.
If you're going to talk about "herd immunity", you need that info to get anywhere.
[1] https://www.medrxiv.org/content/10.1101/2020.04.14.20062463v...
[2] https://abc7ny.com/coronavirus-testing-antibody-new-york-ny/...
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.
[0] https://www.eurekalert.org/pub_releases/2020-08/cp-mcc081720...
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."
(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)
"Heterogeneity in contact structure and individual variation in infectivity, susceptibility, and resistance are key factors..." (emphasis added)
Important data we do not know is chiefly how effective SARS aerosols are and at what range and time.
https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v...
https://www.medrxiv.org/content/10.1101/2020.07.23.20160762v...
https://www.medrxiv.org/content/10.1101/2020.09.26.20202267v...
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
"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.
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?) .
https://www.jimmunol.org/content/early/2020/09/03/jimmunol.2...
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.
https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/comm...
(fyi: they bury the lede on this page: you have to click through to their horribly slow interactive viewer widget to see the multiples.)
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.
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).
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.
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.
You'd like to know if people are wearing masks at church or if family get-togethers are now outdoors.
https://covid19-projections.com/ (Excellent source during these times. Sad to see them deciding to stop moving forward but it's good for now).
See, e.g., https://www.nature.com/articles/s41591-020-1083-1
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%.
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.
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.
EDIT: seriously, downvoting this comment? Can't imagine why and would like to know.
With natural infection, the socially active will be infected and removed first, which lowers the fraction needed.
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).
This is a false binary state space.
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.
Is it:
- everybody will eventually, but much later, get covid and become immune?
- Keep the infected number low until a vaccine is developed?
- Something else?