4 ms·

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 wha

by makomk 6y ago

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.

minitoar 6y ago
I don’t understand why you couldn’t use the average rate of infection to compute this.
- makomk 6y ago
  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.
hyperman1 6y ago
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.
dustinmoris 6y ago
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).
- alistairSH 6y ago
  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.
- makomk 6y ago
  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.)
jameshart 6y ago
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.

by makomk 6y ago

minitoar 6y ago

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

makomk 6y ago
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.

hyperman1 6y ago

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.

dustinmoris 6y ago

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).

alistairSH 6y ago
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.
makomk 6y ago
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.)

jameshart 6y ago

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.