Efficacy in the epidemiological sense is useful for comparing vaccines; higher is better. But it should not be mistaken for a measure of breakthrough probability or the many other things we combine in the everyday meaning of efficacy.
I’ve had a vision of writing a magisterial series to clarify everything about the mathematics of the pandemic, but it looks more like I will, hit-or-miss, do one issue at a time.
I’ve worked with mathematical models for chemical reactions. The math is identical to that of a pandemic – coupled differential equations describing the transformation of one set of things into other things. In the case of the pandemic that transformation is
susceptible people -> infected people -> immune or dead people
Sets of coupled differential equations have become popular for such things since we have gotten enormous computing power. Solving them isn’t easy to do by hand. Epidemiology (and chemical kinetics) grew up with simpler equations to model their processes. And those simpler equations can be good for some things!
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