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Should have been more specific - no, I'm not saying that as an inherent property R0 will vary across time (that'd be R in a simple SEIR model). What I'm saying is that in a naive population where a virus e.g., moves from X1 to X2 and X2 has different env/response, R0 will change.
And separately, yes, R0 *estimates* will vary (likely by a lot) as time goes on. My main point is that R0 isn't some magic number that can be attached to a particular pathogen - it all depends on context. E.g., R0(China) =! R0(UK) for the same virus.
All that's likely to boil down to though is possible changes in contact structure. The other params that feed into R0 *should* be attached to a particular pathogen. With most cases in large urban centers, contact structure is likely similar so R0(China) may approx R0(UK)
Of the main things influencing R0 - contact rate (k), probability of infection (b), and infectious period (d), all will vary based on population, environment, and detection/containment strategies - some more than others.
That's it: R0 is by definition that magic number, fixed & attached to a path. It's defined in an ideal, naive, homogenous, etc population. In theory there's no UK or China, only 1 boring ideal population. In practice... well, it's the kind of stuff that keeps us awake at night.
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