Updating Herd Immunity Models for the US: Implications for the Covid-19 Response (opens in new tab)

When non experts talk about herd immunity they mean herd immunity given no to minimal precautions. This is a well defined concept.

> R0, which is a constant inherent to the virus strain

I think you just devalued your argument.

https://wwwnc.cdc.gov/eid/article/25/1/17-1901_article

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.

> 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.

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

> Each herd immunity level is thus dependent on health measures

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?

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.

[0] https://www.eurekalert.org/pub_releases/2020-08/cp-mcc081720...

There was a recent study of dialysis patients: https://www.thelancet.com/journals/lancet/article/PIIS0140-6...

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."

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)

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?

I believe this model accounts for such individual response:

"Heterogeneity in contact structure and individual variation in infectivity, susceptibility, and resistance are key factors..." (emphasis added)

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.

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.

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.

https://www.jimmunol.org/content/early/2020/09/03/jimmunol.2...

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.

Actual infection count is probably far higher than 8M, isn't it? That's just number of positive tests.

> USA is currently at ~8M infections/recovered

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.

16% is a good estimate of US infection rate.

https://covid19-projections.com/ (Excellent source during these times. Sad to see them deciding to stop moving forward but it's good for now).

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.

See, e.g., https://www.nature.com/articles/s41591-020-1083-1

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%.

200k dead, infection fatality rate estimates seem to vary between 0.1 and 1%, so there should be at least 20m infections.

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.

> 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.

> infections/recovered

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.