Vaccine "critical herd immunity strength".
Let's call it CHIS for now. Assume 100% coverage.
Effectiveness E gives CHI if R ≤ 1/(1−E) = CHIS.
So E=70% gives CHI if R ≤ 3.33.
So CHIS = 3.33.
And E=95% gives CHI if R ≤ 20.
So CHIS = 20.
CHIS is a clearer vaccine metric than E.
With coverage C, the CHIS (Critical Herd Immunity Strength) will be
CHIS(C) = 1/(1−(1−1/CHIS₁₀₀)×C)
where CHIS₁₀₀ is the CHIS for 100% coverage.
C=80% and E=95% gives CHIS(C)=4.17.
C=80% and E=70% gives CHIS(C)=2.27.
So E=70% is inadequate for CHI with C=80% if R=2.5.
Here's a graph of CHIS(C)
— the Critical Herd Immunity Strength for coverage C.
To work out how much R your vaccine can cope with, let
E = efficacy
C = coverage.
Then read the maximum R = CHIS(C) you can keep under control with it.
E.g. E = 70%, C = 80% implies CHIS(C) = 2.27.
Graph of CHIS(C). Zoomed in.
Critical Herd Immunity Strength.
To work out how much R your vaccine can cope with, let
E = efficacy
C = coverage.
From the graph, read the maximum R = CHIS(C) you can keep under control with it.
E.g. E = 70%, C = 80% implies Rmax = CHIS(C) = 2.27.
How much coverage C you need for a vaccine with efficacy E if R = 3.5, which is possibly what B.1.1.7 has.
C = (1−1/R)/E for R = 3.5.
E=95%. C=75.2%.
E=90%. C=79.4%.
E=85%. C=84.0%.
E=80%. C=89.3%.
E=75%. C=95.2%.
E=70%. C=102.0%.
So it's impossible with E=70% or less!
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