6 ms·

> Specifically, once the proportion of recovered in the population reaches 1/(1-R_0), there are no longer enough vectors (infectable indviduals) remaining for a

> Specifically, once the proportion of recovered in the population reaches 1/(1-R_0), there are no longer enough vectors (infectable indviduals) remaining for a serious outbreak to occur. It’s worth noting that this is the same principle that vaccination relies upon; vaccination is just an artificial way to build immunity without having to undergo a full infection. I should learn to never read anything from random people working in areas they don't have any expertise in. This whole section is wrong. 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 is clear when you think for about 1 second about it. The `1/(1-R_0)` value gives you the point where infected people infect 1 more person, it doesn't give the point when the infection stops spreading.

ryankemper 6y ago
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.
dragonwriter 6y ago
> The `1/(1-R_0)` value gives you the point where infected people infect 1 more person Right: it's (after you correct the typo) the point where the number of active cases does not increase over time.
pbourke 6y ago
> I should learn to never read anything from random people working in areas they don't have any expertise in. This is one clear lesson that can be drawn from the pandemic.
- orborde 6y ago
  I don't think so. Consider that many governments with professional public health departments, including those of the richest countries in the world, downplayed the unfolding disaster, completely blew it on containment as a result, and are now reduced to using _extremely_ expensive lockdown measures to try to buy time until someone can come up with a better idea. Meanwhile, plenty of randos on the internet did the straightforward epidemiological math in January/February and correctly deduced what was coming. I think a clearer lesson is that, sometimes, the designated professional experts will fail to outsmart a fairly simple and very well known system of differential equations. If you find this conclusion terrifying, well, I agree.
  - throwaway0a5e 6y ago
    >Consider that many governments with professional public health departments, including those of the richest countries in the world, downplayed the unfolding disaster, completely blew it on containment as a result Governments are ultimately run on a day to day basis by politicians. Proactive measures to prevent a crisis are a much tougher action to justify, especially if they negatively affect people in a way more direct than just spending their tax dollars, than reacting to a crisis. If anything I think this crisis should teach us something about how governments make choices.
    - icebraining 6y ago
      It can go both ways; here in Portugal the government closed stuff like schools despite the National Public Health Council saying that was disproportionate.
  - icebraining 6y ago
    When you have enough people throwing guesses around, inevitably some are bound to get it right.

ryankemper 6y ago

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.

dragonwriter 6y ago

> The `1/(1-R_0)` value gives you the point where infected people infect 1 more person Right: it's (after you correct the typo) the point where the number of active cases does not increase over time.

pbourke 6y ago

> I should learn to never read anything from random people working in areas they don't have any expertise in. This is one clear lesson that can be drawn from the pandemic.

orborde 6y ago
I don't think so. Consider that many governments with professional public health departments, including those of the richest countries in the world, downplayed the unfolding disaster, completely blew it on containment as a result, and are now reduced to using _extremely_ expensive lockdown measures to try to buy time until someone can come up with a better idea. Meanwhile, plenty of randos on the internet did the straightforward epidemiological math in January/February and correctly deduced what was coming. I think a clearer lesson is that, sometimes, the designated professional experts will fail to outsmart a fairly simple and very well known system of differential equations. If you find this conclusion terrifying, well, I agree.
- throwaway0a5e 6y ago
  >Consider that many governments with professional public health departments, including those of the richest countries in the world, downplayed the unfolding disaster, completely blew it on containment as a result Governments are ultimately run on a day to day basis by politicians. Proactive measures to prevent a crisis are a much tougher action to justify, especially if they negatively affect people in a way more direct than just spending their tax dollars, than reacting to a crisis. If anything I think this crisis should teach us something about how governments make choices.
  - icebraining 6y ago
    It can go both ways; here in Portugal the government closed stuff like schools despite the National Public Health Council saying that was disproportionate.
- icebraining 6y ago
  When you have enough people throwing guesses around, inevitably some are bound to get it right.