Quantitative Editor, @FiveThirtyEight | PhD, @LSEGovernment | 
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But those assumptions are important to get a model that fits well out of sample. So this should be guided based on your epidemiological knowledge, your understanding of how the data was collected, and analyses of model fit.
3) Now, the "cubic fit" part: a) you're assuming a very particular functional form. And b) using polynomials to extrapolate is particularly iffy because the edge behavior of polynomials is notoriously finicky (https://en.wikipedia.org/wiki/Runge%27s_phenomenon …). This is a bad way to fit a flexible model.
4) This *could* be something more complicated like a gam with a cubic spline, but all we have to go on is the phrase "cubic fit", so... who knows? And it may well have similar issues.
5) I think a lot of the frustration here is that this hugely policy-relevant model seems like it might be based on something my third stats class told me not to do, and we don't have the information necessary to evaluate it.
@jjcherian Weierstrass approximation theorem making an appearance
Not to mention that a cubic function, necessarily, goes to +INF in one direction of time and -INF in the other, neither of which are (for obvious reasons) remotely plausible.
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