> This is why the spread of a virus like this is a logistic curve, not an exponential.

More on this by 3Blue1Brown: https://www.youtube-nocookie.com/embed/Kas0tIxDvrg

Somewhere after, or around, thee 5 minute mark:

"true exponentials are basically non-existent in real life"

The reality is even more complicated - sure, a logistic curve is a reasonable fit if we assume that the data is accurate and the population homogeneous and well mixed, but in practice things get more complicated quickly. There's a huge network of potential contacts, with a large degree of heterogeneity and important subcomponents at multiple geographic scales. In addition, the network is dynamic, not static, so that both highly granular and population scale phenomena can change the contact distribution. Two important questions are:

1. What can we actually measure with confidence to relate to a model of interest 2. At what level of sophistication is it feasible to actually model things

Neither question is particularly straightforward in the face of ongoing epidemics.

The data from China almost perfectly follows a logistic curve. Unfortunately, extrapolating such a smooth function is pretty much impossible before it starts saturating anyway.

For sure, but the problem is that innumerable true situations might give rise to a given "observed" logistic curve - something that you can describe with two parameters arose from a mix of incomprehensibly complex transmission dynamics and dauntingly difficult (and often hidden) observation mechanisms. The result is that, even though after the fact we can often achieve a good fit with simple models, there's little reason to expect that simple models would have been generally predictive - the feedback loop even includes the models, since they might inform public health policy!

This isn't to say that modelling isn't useful, but that forecasting a novel infection while it's ongoing is really, really, really hard.

Edit: Also, I’d be interested to see a comparison of the fit between a typical logistic, four parameter logistic, Gompertz etc. Not all sigmoids are the same.

Gompertz type 2 fits somewhat better.

Ultimately for such complex things like spread with barriers Tsalis statistics are good. That could mean q-Weibull distribution.

Not even remotely:

1) Number of cases is not flat. Even by now.

2) There was a slowed growth in late cases.

It fits Weibull statistics. Late spread is random but responds to distance. (A'la Rayleigh.)

Finally! I have been almost killed for calling this out. It's like some people believe epidemiologists haven't figured that out yet. And it does make a huge difference, whether the underlying function has a natural peak or not.

you're technically right, but i think from a policy making standpoint it doesn't matter because it's the exponential part that needs to be contained by policy and not the saturation part. this is where the hard decisions have to be made. if no decisions are made, saturation starts to happen when the game is lost.