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Comment by anovikov | Hacker News Reader

This is a rather meaningless, narrow-minded claim. Herd immunity is not a "binary" state which you either have in a country, or not. It doesn't magically turn from "0" to "1" when you cross a certain threshold of % of immunised population. It comes gradually when reproduction rate in different groups of population gradually crosses under 1, until (ideally) it does so for entire population.

In case of Israel, certainly there is "herd immunity" for majority of population and certainly there is lack of it for significant minority groups.

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You are wrong. This actually is "binary" state.

The reproduction rate is either higher than 1 or lower than 1. In any population, if the reproduction rate is lower than 1 the virus will be in decline BY DEFINITION.

Now, some subpopulations might see reproduction factor higher than one but that is still not nullifying the previous statement.

For example, the world might reach heard immunity even if Afghanistan and Russia are still seeing increase in cases.

When they say "Israel" reached herd immunity they mean that, overall, the number of cases in Israel is falling. That's basically what it means.

Additional assumption about "herd immunity" is that this decline will continue even if extraordinary restrictions are lifted, which means that the reproduction factor is low enough on basis of peoples' acquired immunity to be under 1.0000 even without restrictions.

No, this really isn't a binary state. In order for the reproduction rate to be a single, fixed figure which only depends on the level of immunity - which is what you need in order for herd immunity to be a binary thing - every person needs to be exactly as likely to infect every other person. Obviously this isn't remotely true, at all.

I don’t understand why you couldn’t use the average rate of infection to compute this.

Suppose that cases are going down almost everywhere and you compute the average and calculate R from that, getting a nice reassuring number below 1 - but there's some part of society, somewhere, where cases are still increasing exponentially. Just a small fraction of cases initially. Over time, the number of cases in the parts of society where Covid is under control decrease whilst the cases in the parts where it isn't increase, until inevitably the rate at which cases grow is completely dominated by the bits where Covid is out of control, even when those started off so small as to have almost no effect on the overall average. That's why you can't just rely on the average. (In fact, I'm pretty sure the fraction of cases which are caused by the parts where Covid is still under control should decrease exponentially.)

Also, remember that the effective rate of reproduction can easily vary by huge amounts between different parts of society, for example if some age groups are almost completely vaccinated and others are almost completely unvaccinated.

These requirements are too strict. The main requirement is that average reproduction rate stays reasonably well below 1. If it fluctuates between 0.1 and 0.9 in time or between people, you still have heard immunity.

Presumably, Interesting things happen around 1.0, where the instability can push you either way. Hence heard immunity is almost a binary state.

This is wrong. Let's take children as an example. COVID could spread at a rate higher than 1 in schools, but if all teachers, parents and grandparents have been vaccinated (at a high uptake) then the spread in children won't spill into the older generations and therefore the overall reproduction rate might still be below 1. This is really just simple maths and I don't understand how one could make it easier to understand. It's literally a single number with a binary meaning:

R > 1: Infections rising R < 1: Infections declining

If we remove all restrictions and remain R < 1 due to vaccination then we have by definition reached herd immunity (key word is herd, not individual).

I believe you and the OP are talking past each other. The OP didn't reference R value, just herd immunity.

Take the US...

Certain sub-populations could very well have herd immunity within that group. A group like meat-packing plant employees and their families. They've all had COVID or been vaccinated.

But, within the group of "white collar workers who can afford to remain socially distant", we could be a long way from herd immunity - this group has remained distant (low number of past infections) and hasn't been eligible for vaccination (<65 years old, mostly healthy).

Yes, at a macro level, herd immunity is mostly binary. But, over a population of 300,000,000, there's a lot of room for sub-populations with differing levels of immunity.

This is in fact the whole problem: "COVID could spread at a rate higher than 1 in schools, but if all teachers, parents and grandparents have been vaccinated (at a high uptake) then the spread in children won't spill into the older generations and therefore the overall reproduction rate might still be below 1." Yes, in this scenario the reproduction rate R could initially be below 1 making it look like we had herd immunity and could declare victory but it would inevitably increase to above 1, meaning an exponential growth in cases, even if all restrictions and everyone's behaviour was the same as when it was below 1. Here's why.

Assume for convenience that Covid cases double each week in schools and halve each week in adults, there's no spread from one group to the other, and almost all cases are in adults initially. Initially we measure R and it's firmly below one, because almost all cases are in adults and those are declining rapidly. After one week there are twice as many cases in children and half as many in adults, after two there are four times and a quarter, eight times and one-eighth... and pretty soon the number of remaining cases in adults are so few any further reduction can't possibly compensate for the exponential increase in schools, and overall cases are growing exponentially and fast. Our declaration of victory was dangerously premature.

The exact numbers don't even matter; so long as the reproduction rate is firmly below 1 in one group and firmly above 1 in the other, the group where cases are shrinking will make up an exponentially decreasing proportion of total cases and the overall rate of spread will quickly become determined by the group where cases are still growing. (The assumption of no spread from one group to the other doesn't matter either; it just makes the explanation slightly simpler.)

That’s like saying that in order for temperature to be a fixed figure which depends on pressure, which is what you need for condensation to be a thing, every molecule needs to be exactly as likely to collide with every other molecule. Therefore liquid/gas can’t be a binary state.

Phase transitions in large scale systems resulting from changes in the average behavior of individual elements are a real thing. An infection is an unstable dynamic system which tends to different states depending on whether the mean R is greater or less than one.

I agree that it is a binary state (under or over 1), but over time, it isn't a fixed number that depends only on the achieved immunity level, it also depends on people's risk-taking behaviour, which brings there a whole lot of nasty feedback loops.

Well, if herd immunity is achieved only by a part of population, then decline will continue only to a point where all cases in that part of population will end, but stay with the rest of them. In practice because groups of population are not isolated from one another it just means that amount of cases will decline to a certain level (dictated by time which it takes for the natural immunity to wear out, and fraction of population that hasn't reached herd immunity).

In practice it may mean that virus is gone as a "problem" (remaining case load, especially considered that most vulnerable people are vaccinated to a higher degree in all groups of population, will be manageable for the healthcare system). But cases will never go to zero, and some unlucky people even most vaccinated groups will still get sick.

Now on the level of individual country, it's not a big deal. On the level of the world ("if all countries apart from Afghanistan and Russia vaccinate almost all people, reach herd immunity in all groups of population, and their case numbers will go to zero"), it is very different. If we still have say 3% of the world population with the virus actively circulating, they will give us a vaccine-resistant strain sooner rather than later, and we are back to square one.

And this is what i hate most about Covid vaccination campaign: we need most of all to vaccinate the countries that worry the least about Covid: poor African countries with very young population - that have almost no symptomatic cases and very few deaths, for who Covid is really not a problem at all, especially compared to all their other troubles, health-related and otherwise. These people will have unlimited circulation of virus because they don't worry, and will create new and new strains every while until one of them achieves vaccine escape. And they can't see vaccinations as anything but blatant intrusion into their internal affairs ("these white people who want to inject us with some stuff for THEIR benefit").

Incredibly enough, this kind of phenomenon really is almost magically turning from "0" to "1" when a certain threshold is met. This goes by several names depending on the field but "phase transition" and "percolation" are usual.

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