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You're confusing R0 (the basic reproduction number, defined theoretically at time zero) with the reproduction number at time t (sometimes called the effective reproduction number).
Yeah, I'm aware of the difference between the basic and effective reproduction number, but no, I'm still referring to R0 given that the virus is still spreading through a naive population and for R=R0x, we can largely ignore x (for now). This will of course change and R < R0.
2.5m after, herd-immunity matters. The observed epi is now an aggregated mix of epis happening at various stages & places. We now have parallel epis with very different durations. Also relevant: control keeps these spatially disaggregated, so homogenous assumptions collapse.
Exactly. Across a large enough epidemic these heterogeneities even out such that comparing R0 among epidemics is a useful way of comparing transmissibilities (beta) and planning interventions. Right now, the R0 is very context sensitive. 1/2
R0 was defined as an invariant property of a homogeneous epidemic, explicitly to distinguish it from time-dependent values like R. If host population properties such as contact rate & density vary through time, then R makes more sense than R0.
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