Quote:
Originally Posted by NickMPK
This looks right to me; I stand corrected!
And it really demonstrates how even modest progress toward herd immunity can have a huge effect on reducing total future infections.
Yes, it's a factor - but the main thing is making sure a lot of people don't have it. As the chart you're replying to shows, if 10% of the population have it when you switch to R0.9, then it basically stops at around 35% immune / 65% susceptible.
If you do that when 1% have it, then it's different:
Stg R0 infected susceptible, R new infections
1 0.9 1.000 99.000 0.891 0.891
2 0.9 0.891 98.109 0.883 0.787
3 0.9 0.787 97.322 0.876 0.689
4 0.9 0.689 96.633 0.870 0.599
99 0.9 0.000 92.633 0.834 0.000
You finish with only 7.4% infected and 92.633 still immune.
If people are interested, here are a few more for different R0 levels from the same spreadsheet (with really high R0s, modelling it as a discrete generations starts to cause problems - so with R0 of 20, 5% infected shouldn't actually infect everyone else, as towards the end of their infectious period they would be running into more and more newly infected people and not just uninfected people).
R0=1.1
Stg R0 infected susceptible, R new infections
1 1.1 1.000 99.000 1.089 1.089
2 1.1 1.089 97.911 1.077 1.173
3 1.1 1.173 96.738 1.064 1.248
4 1.1 1.248 95.490 1.050 1.311
5 1.1 1.311 94.179 1.036 1.358
99 1.1 0.000 75.461 0.830 0.000
(Herd immunity strategy with R0=1.1 means 24.5% get it)
R0=1.3
Stg R0 infected susceptible, R new infections
1 1.3 1.000 99.000 1.287 1.287
2 1.3 1.287 97.713 1.270 1.635
3 1.3 1.635 96.078 1.249 2.042
4 1.3 2.042 94.036 1.222 2.496
5 1.3 2.496 91.540 1.190 2.971
99 1.3 0.000 53.394 0.694 0.000
(Herd immunity with R0=1.3 means 46.7% get it)
R0=2
Stg R0 infected susceptible, R new infections
1 2 1.000 99.000 1.980 1.980
2 2 1.980 97.020 1.940 3.842
3 2 3.842 93.178 1.864 7.160
4 2 7.160 86.018 1.720 12.317
5 2 12.317 73.701 1.474 18.156
99 2 0.000 12.618 0.252 0.000
(Herd immunity strategy with R0=2 means 87.3% get it)
As an alternative - let's imagine we've got 1% infected and 49% have already had it, we declare "herd immunity" and remove the controls. What happens next depends on the value of R0.
R0=4
Stg R0 infected susceptible, R new infections
1 4 1.000 50.000 2.000 2.000
2 4 2.000 48.000 1.920 3.840
3 4 3.840 44.160 1.766 6.783
4 4 6.783 37.377 1.495 10.141
5 4 10.141 27.236 1.089 11.048
6 4 11.048 16.188 0.648 7.154
7 4 7.154 9.034 0.361 2.585
8 4 2.585 6.449 0.258 0.667
9 4 0.667 5.782 0.231 0.154
99 4 0.000 5.583 0.223 0.000
(In the end 94.6% get it - though the discrete generations model is possibly breaking down here)
R0=3
Stg R0 infected susceptible, R new infections
1 3 1.000 50.000 1.500 1.500
2 3 1.500 48.500 1.455 2.183
3 3 2.183 46.318 1.390 3.033
4 3 3.033 43.285 1.299 3.938
5 3 3.938 39.347 1.180 4.648
99 3 0.000 17.091 0.513 0.000
(In the end 82.9% get it)
R0=2.5
Stg R0 infected susceptible, R new infections
1 2.5 1.000 50.000 1.250 1.250
2 2.5 1.250 48.750 1.219 1.523
3 2.5 1.523 47.227 1.181 1.799
4 2.5 1.799 45.428 1.136 2.043
5 2.5 2.043 43.385 1.085 2.216
99 2.5 0.000 27.291 0.682 0.000
(In the end 82.7% get it)
R0=2
Stg R0 infected susceptible, R new infections
1 2 1.000 50.000 1.000 1.000
2 2 1.000 49.000 0.980 0.980
3 2 0.980 48.020 0.960 0.941
4 2 0.941 47.079 0.942 0.886
5 2 0.886 46.193 0.924 0.819
99 2 0.000 40.331 0.807 0.000
(In the end 59.7% get it)
R0=1.5
Stg R0 infected susceptible, R new infections
1 1.5 1.000 50.000 0.750 0.750
2 1.5 0.750 49.250 0.739 0.554
3 1.5 0.554 48.696 0.730 0.405
4 1.5 0.405 48.291 0.724 0.293
5 1.5 0.293 47.998 0.720 0.211
99 1.5 0.000 47.261 0.709 0.000
(In the end 52.7% get it)
So the overall point of the above is - that what herd immunity means is itself a function of the expected R0 after it's all over.
If people are imagining "after this is all over" to look like how things were before, then herd immunity means something like 80-90% already immune (realistic only though mass vaccinations). Otherwise, the question is how can society run with an R0 of less than 1, or less than 1.2 or something? Will masks and 360 degree testing of all confirmed cases be enough? Hope so.
Anyway, this is why I keep saying I fully expect to still be wearing a mask in 2020.
Quote:
Originally Posted by Xenoblade
Well I’m glad it is a wake up call for some
btw people saying to not go for herd immunity because it won’t work because people don’t make antibodies or whatever, what’s your solution? If herd immunity does not work, vaccines won’t work
I'm pretty sure it will work. Even if you get a mutated version then there will be some partial immunity. The problem is a lot of people will die while herd immunity is being established.