4 ms·

Yes, actually. That’s right at the inflection point where each added percent effectiveness is maximally beneficial to herd immunity. E.g. the difference from 85

Yes, actually. That’s right at the inflection point where each added percent effectiveness is maximally beneficial to herd immunity. E.g. the difference from 85% to 95% is much less important than 60% -> 70%.

mlyle 6y ago
?? This is a crazy way to look at it. If R0 is 2.5, then you need to vaccinate (1 - 1/2.5) / .95 of the population = 63% to reach herd immunity. For a 60% effective vaccine, you get (1 - 1/2.5) / .6 = 100% of the population. Yes, the slope is slightly different but the rolloff is exceptionally gentle. There is a huge difference in practicality between even an 85% and 95% effective vaccine (70% of the population vs. 63% of the population). Not to mention that none of what we've measured is differences in transmissibility; it's quite possible that a 70% effective-against-symptomatic-illness vaccine only mitigates transmission rates by 35%, and thus can't reach herd immunity at any level of vaccination.
- thesz 6y ago
  And for 50% effective vaccine and R0 of 2.5, one has to vaccinate what, (1-1/2.5)/0.5=1.2 or 120% of population? Please, correct your math. It is weirdly off.
  - sanxiyn 6y ago
    50% effective vaccine could lower R0 of 2.5 to 1.25 (2.5 * 50% = 1.25). That's R0 > 1, so it can't stop transmission.
  - clausz 6y ago
    No, it's not. It only means that with these given numbers it is impossible to reach herd immunity.
    - garmaine 6y ago
      Not impossible, just can't be done by vaccination alone. The remaining required percentage of the population would have to get immunity from getting sick. This is what I was getting at in the grandparent post. 50% -> 60% and 85% -> 95% might both seem like they protect 10% more of the population, but the qualitative effect on the spread of the pandemic and be quite different. 60% might be enough to get herd immunity (with masks and social distancing), while 50% is not. Both 85% and 95% are definitely enough to get herd immunity, so to some extent that added protection matters less.
      - mlyle 6y ago
        It's still not any kind of "inflection point". The difference between 0 and 5% is an even sharper slope-- from infinity to 1200% of the population ;) Also-- all we know about is effects on symptomatic illness and we can't be sure there's any large transmission benefit (and if there is, it's probably smaller than the efficacy against symptomatic illness). If the virus is still circulating in volume, the difference between a 95% effective vaccine and a 70% vaccine is a further 6x reduction in risk for the individuals that have it. Every little bit helps, but a really high efficacy is very nice to have.
  - mlyle 6y ago
    Thought experiment: how much of the population do you think you need to immunize with a 0.1% effective vaccine to stop the virus from circulating? I find it's helpful, when I see something counterintuitive to me in math, to consider the extreme cases. Obviously a 0.1% effective vaccine won't be able to attain herd immunity. Within a set of simplified assumptions, you need to stop 60% of the transmission to get fewer infected each generation from a R0=2.5 disease, and vaccines with less than 60% efficacy against transmission cannot stop 60% of the transmission themselves (though they certainly would still help).

mlyle 6y ago

?? This is a crazy way to look at it. If R0 is 2.5, then you need to vaccinate (1 - 1/2.5) / .95 of the population = 63% to reach herd immunity. For a 60% effective vaccine, you get (1 - 1/2.5) / .6 = 100% of the population. Yes, the slope is slightly different but the rolloff is exceptionally gentle. There is a huge difference in practicality between even an 85% and 95% effective vaccine (70% of the population vs. 63% of the population). Not to mention that none of what we've measured is differences in transmissibility; it's quite possible that a 70% effective-against-symptomatic-illness vaccine only mitigates transmission rates by 35%, and thus can't reach herd immunity at any level of vaccination.

thesz 6y ago
And for 50% effective vaccine and R0 of 2.5, one has to vaccinate what, (1-1/2.5)/0.5=1.2 or 120% of population? Please, correct your math. It is weirdly off.
- sanxiyn 6y ago
  50% effective vaccine could lower R0 of 2.5 to 1.25 (2.5 * 50% = 1.25). That's R0 > 1, so it can't stop transmission.
- clausz 6y ago
  No, it's not. It only means that with these given numbers it is impossible to reach herd immunity.
  - garmaine 6y ago
    Not impossible, just can't be done by vaccination alone. The remaining required percentage of the population would have to get immunity from getting sick. This is what I was getting at in the grandparent post. 50% -> 60% and 85% -> 95% might both seem like they protect 10% more of the population, but the qualitative effect on the spread of the pandemic and be quite different. 60% might be enough to get herd immunity (with masks and social distancing), while 50% is not. Both 85% and 95% are definitely enough to get herd immunity, so to some extent that added protection matters less.
    - mlyle 6y ago
      It's still not any kind of "inflection point". The difference between 0 and 5% is an even sharper slope-- from infinity to 1200% of the population ;) Also-- all we know about is effects on symptomatic illness and we can't be sure there's any large transmission benefit (and if there is, it's probably smaller than the efficacy against symptomatic illness). If the virus is still circulating in volume, the difference between a 95% effective vaccine and a 70% vaccine is a further 6x reduction in risk for the individuals that have it. Every little bit helps, but a really high efficacy is very nice to have.
- mlyle 6y ago
  Thought experiment: how much of the population do you think you need to immunize with a 0.1% effective vaccine to stop the virus from circulating? I find it's helpful, when I see something counterintuitive to me in math, to consider the extreme cases. Obviously a 0.1% effective vaccine won't be able to attain herd immunity. Within a set of simplified assumptions, you need to stop 60% of the transmission to get fewer infected each generation from a R0=2.5 disease, and vaccines with less than 60% efficacy against transmission cannot stop 60% of the transmission themselves (though they certainly would still help).