Read on Twitter
Again there’s an essentially ‘causal’, model-based point behind the per capita or not arguments - if you non-dimensionalise appropriately, all countries follow the same dynamics, and the basic equations tell you the appropriate initial condition is the fraction of pop https://twitter.com/ct_bergstrom/status/1249930299258990592
Eg quick google books search for an example explanation gives:
Notice how the appropriate initial condition falls out naturally. Also, there are now only two key non-dimensional parameters (in this model) - R0 and the initial condition (as a fraction of susceptible). Visualisations are typically targeted at (effective) R0
(Also...notice that identifiability problems are potentially very real when trying to estimate individual parameters of the full model...)
(And that S(0) is really the S(0) for a particular outbreak...)
