Small moan about models and parameters in COVID. R - the number of infections each person makes on average is a parameter but it is also something that one can measure. Each infected person has their own "R" - it is a count - and one could in theory measure all these little Rs
This R is both something one can measure and the average R, or the distribution of R is often components of model. It is a "real measurable thing" and it is "part of our COVID models".
You might want to model other things; one is the distribution of how R varies between people/events. A sensible choice is a negative binomial. Often people use k as a parameter (in fact, in other uses, they often use the letter r as a parameter, but this would be confusing!)
k here is not measureable in the same way as R. It doesn't have meaning on an individual level and one can't subdivide k into different groups. You fit k with data. k is part of COVID models, but a modelling choice not a measurable thing at the limit.
Does this matter? Not much I suspect. But ... it's good to keep these things straight.
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