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I'm sure you're getting weary at this point, but I really need your help understanding what you're saying here, because to me it seems supremely untrue. First,

I'm sure you're getting weary at this point, but I really need your help understanding what you're saying here, because to me it seems supremely untrue. First, `1/1-R_0`. This is exactly what Wikipedia says: https://en.wikipedia.org/wiki/Herd_immunity#Mechanics https://en.wikipedia.org/wiki/Herd_immunity#Mechanics And it makes intuitive sense that once you infect <= 1.00 people, growth is no longer exponential. So I don't think that point is wrong at all. > The idea that vaccination and epidemics need the same percent of immunity is completely 100% wrong. An active epidemic is going to infect way more people before dying out than the simple, naive herd immunity calculation will give you. In fact, while an r0 of 2 indicates that you get herd immunity with just 50% of the population, a typical active epidemic with the same r0 would infect 80+% before dying out. This doesn't make any sense to me. Vaccination is just an artificial way to build immunity. So I don't understand your active epidemic point at all. Or put another way, as the proportion of % recovered goes up, we start approaching the eventual limit where `1/1-R_0`->1. That is to say, in your example we start with R_0 = 2, then as people recover that value slowly starts decreasing until it hits 1 at the herd immunity threshold. It's not clear to me what the discrepancy you're detecting is here.

danieltillett 6y ago
Even when the R0 reaches 1.0 those who are infected will still infect one more person (on average). Infections continue to happen after the R0 is below 1.0.
- ryankemper 6y ago
  Thanks, that does make intuitive sense. I wonder for a virus like SARS-CoV-2 that has a high R_0 and thus requires maybe 80% of the population to be immune for full herd immunity, if that means that the overshoot would be pretty mild?
  - danieltillett 6y ago
    It would mean the overshoot would likely go close to 100%, but it is complex to model as not everyone is equally likely to be infected - basically the population is not uniform. Epidemiologist do model this, but it requires relatively complex models.
ruarai 6y ago
This is called 'overshoot'. See here for a good explanation https://twitter.com/CT_Bergstrom/status/1252077930286444545 https://twitter.com/CT_Bergstrom/status/1252077930286444545
- ryankemper 6y ago
  Thanks. That was helpful. So then, it does seem that if we successfully contained the virus, and then avoided infection spread until a hypothetical future vaccine is developed, that we could avoid the number of infections required by some amount. Just to tie it back to the broader lockdown vs not lockdown debate, we could probably say that a successful full containment strategy+vaccination could decrease the net area under the curve. As far as policy is concerned I still think the costs of locking down for that long (particularly given that the time is unbounded) is not worth it, but that is a very valid point that I will need to circle back and weave into the document.
  - sumfoni 6y ago
    So you are telling me, that you write an article with misstakes and think you should be the person making statements because you are able to write an article? And you also think, that politicians are doing an economycal suicide just because they like it? Srsly, wouldn't you assume and shouldn't you assume, that there are experts calculating and estimating that shit on every single day and trying there best to find a reasonable way out of this?
    - ryankemper 6y ago
      > So you are telling me, that you write an article with misstakes and think you should be the person making statements because you are able to write an article? Yes, I am a person that makes and is currently making mistakes. > And you also think, that politicians are doing an economycal suicide just because they like it? I analyzed the "game theory" of this a bit here: https://www.ryankemper.io/post/2020-04-29-the_case_for_ending_lockdown/#how-did-we-get-here https://www.ryankemper.io/post/2020-04-29-the_case_for_endin... > Hanlon’s Razor is very relevant here; we think it is not reasonable to assume that they were trying to usher in a techno-totalitarian state. Rather, they were trying to prevent mortality, but their incentive structure is such that it is much worse to have done nothing and later find out that the virus was worse than we thought, than what actually happened, which is to have undertaken actions that were self-destructive and then discovered that the virus was way less deadly than we thought.
xscott 6y ago
> First, `1/1-R_0`. This is exactly what Wikipedia says: https://en.wikipedia.org/wiki/Herd_immunity#Mechanics https://en.wikipedia.org/wiki/Herd_immunity#Mechanics I have no expertise in this area, but Wikipedia does not say: 1/(1 - R_0) It's: 1 - (1/R_0) Which makes much more sense to me on a math footing. You should probably fix that in your article so it doesn't confuse other pedants like myself.
- ryankemper 6y ago
  Doh! Thanks for catching that. That is a really glaring mistake on my part. (The irony in me having said it was "exactly" what Wikipedia says is not lost on me :P) https://gitlab.com/ryankemper/writings/-/commit/093ade62944768b5cd8627aaf81f94cc613483ff https://gitlab.com/ryankemper/writings/-/commit/093ade629447...
  - xscott 6y ago
    No worries - it was clearly just a typo :-)
    - ryankemper 6y ago
      It is fun to imagine the negative herd immunity threshold implied by the erroneous form of the equation though :P Say R0 is 2, 1/(1 - R0) means that we already hit herd immunity before SARS-CoV-2 even existed!
      - xscott 6y ago
        The frightening one for me was R0 == 1: Basically, we'd need a positive or negative infinite percentage of people to be infected depending on which direction you approach it from.

danieltillett 6y ago

Even when the R0 reaches 1.0 those who are infected will still infect one more person (on average). Infections continue to happen after the R0 is below 1.0.

ryankemper 6y ago
Thanks, that does make intuitive sense. I wonder for a virus like SARS-CoV-2 that has a high R_0 and thus requires maybe 80% of the population to be immune for full herd immunity, if that means that the overshoot would be pretty mild?
- danieltillett 6y ago
  It would mean the overshoot would likely go close to 100%, but it is complex to model as not everyone is equally likely to be infected - basically the population is not uniform. Epidemiologist do model this, but it requires relatively complex models.

ruarai 6y ago

This is called 'overshoot'. See here for a good explanation https://twitter.com/CT_Bergstrom/status/1252077930286444545 https://twitter.com/CT_Bergstrom/status/1252077930286444545

ryankemper 6y ago
Thanks. That was helpful. So then, it does seem that if we successfully contained the virus, and then avoided infection spread until a hypothetical future vaccine is developed, that we could avoid the number of infections required by some amount. Just to tie it back to the broader lockdown vs not lockdown debate, we could probably say that a successful full containment strategy+vaccination could decrease the net area under the curve. As far as policy is concerned I still think the costs of locking down for that long (particularly given that the time is unbounded) is not worth it, but that is a very valid point that I will need to circle back and weave into the document.
- sumfoni 6y ago
  So you are telling me, that you write an article with misstakes and think you should be the person making statements because you are able to write an article? And you also think, that politicians are doing an economycal suicide just because they like it? Srsly, wouldn't you assume and shouldn't you assume, that there are experts calculating and estimating that shit on every single day and trying there best to find a reasonable way out of this?
  - ryankemper 6y ago
    > So you are telling me, that you write an article with misstakes and think you should be the person making statements because you are able to write an article? Yes, I am a person that makes and is currently making mistakes. > And you also think, that politicians are doing an economycal suicide just because they like it? I analyzed the "game theory" of this a bit here: https://www.ryankemper.io/post/2020-04-29-the_case_for_ending_lockdown/#how-did-we-get-here https://www.ryankemper.io/post/2020-04-29-the_case_for_endin... > Hanlon’s Razor is very relevant here; we think it is not reasonable to assume that they were trying to usher in a techno-totalitarian state. Rather, they were trying to prevent mortality, but their incentive structure is such that it is much worse to have done nothing and later find out that the virus was worse than we thought, than what actually happened, which is to have undertaken actions that were self-destructive and then discovered that the virus was way less deadly than we thought.

xscott 6y ago

> First, `1/1-R_0`. This is exactly what Wikipedia says: https://en.wikipedia.org/wiki/Herd_immunity#Mechanics https://en.wikipedia.org/wiki/Herd_immunity#Mechanics I have no expertise in this area, but Wikipedia does not say: 1/(1 - R_0) It's: 1 - (1/R_0) Which makes much more sense to me on a math footing. You should probably fix that in your article so it doesn't confuse other pedants like myself.

ryankemper 6y ago
Doh! Thanks for catching that. That is a really glaring mistake on my part. (The irony in me having said it was "exactly" what Wikipedia says is not lost on me :P) https://gitlab.com/ryankemper/writings/-/commit/093ade62944768b5cd8627aaf81f94cc613483ff https://gitlab.com/ryankemper/writings/-/commit/093ade629447...
- xscott 6y ago
  No worries - it was clearly just a typo :-)
  - ryankemper 6y ago
    It is fun to imagine the negative herd immunity threshold implied by the erroneous form of the equation though :P Say R0 is 2, 1/(1 - R0) means that we already hit herd immunity before SARS-CoV-2 even existed!
    - xscott 6y ago
      The frightening one for me was R0 == 1: Basically, we'd need a positive or negative infinite percentage of people to be infected depending on which direction you approach it from.