A useful contribution. Reminder: There is nothing natively logarithmic about f' vs f (what they're ~plotting), unlike f'(t) vs t and f(t) vs t, which have have a fundamental logarithmic expectation (should be linear, or near-linear, in semi-log space). https://www.youtube.com/watch?time_continue=2&v=54XLXg4fYsc&feature=emb_logo

The choice of log-log plotting is for convenience with inputs varying by orders of magnitude, and to make the 'animation' representation of t approximately linear (so the animated plotting point moves nearly linearly with time).

Log-log plotting likely tends to hide variations in slope, which may be partly why they all plot on top of each other.

But they are actually surprisingly similar (just not *that* similar); that is also seen in semi-log - time plots.

Technically, what we're plotting is log(~f') vs log(f), where f is accumulated cases and ~f' is a smoothed trailing numerical estimate of the rate of change (in cases per week).

~f'(t) = (f(t) - f(t-7))/1.0, cases per week, t in days.

When f is exponential in t, f' = k.f, so f' vs f will be linear -- on a linear plot, and in log-log space. Linearised plots are useful to humans because we are linear thinkers; we notice deviations from linear, when we mightn't have recognised a deviation from a curving function.

So they provide a striking visualisation of change, but they may not be useful for elucidating its parameters (timing, degree). This differential plotting effort might even tend to hide that through strong smoothing (the weekly moving average) and compressed log-log plotting.

Interestingly, the underlying exponential process here, R₀-𝜏 epidemic propagation, is not in f, accumulated cases, but in fₙ, new cases (it is new cases that propagate, not accumulated cases).

Which means that tight exponential behaviour is actually in fₙ' = kₙ.fₙ (which is the second derivate of accumulated cases, f'' = kₙ.f'). The exponential in accumulated cases only arises because the integral of an exponential is (eventually) also an exponential.

So the smarter differential plot here should actually be ~fₙ' vs fₙ, or log(~fₙ') vs log(fₙ), except that a numerical estimate of the rate of change in new cases (~fₙ') is going to be horribly noisy, so need even stronger smoothing.

May twig that I don't much like differential plotting, on the whole. Which is not to say don't.

If know the expected underlying function (fₙ' = kₙ.fₙ due to R₀-𝜏 propagation, hence fₙ(t) = fₙ(0).eᵏₙᵗ) ... is generally best to *plot that*.