Logistic function better. Or an asymmetrical version of it.

Why? Better at what?

Nothing special about this function, meiner meinung nach.

The logistic function comes out of many math biol models (as well as other fields), including some epid. models. Or it's at least a decent approximation to what comes out of these models. So it's not unreasonable to fit that function. By "asymmetrical" I just mean that the basic logistic function doesn't capture the asymmetry in the growth and decay phrases of an epidemic. Hence needing a slightly more general function for fitting.

But taking an arbitrary function and fitting it seems a bit silly. It's usually nice to have some plausible excuse for a functional form!

I don't know what the "cubic" model does. But cubics do go off to plus/minus infinity, so I hope it's not modelling deaths!

I've been thinking about this and I agree. From an approximation theory viewpoint cubic polynomials are untrustworthy (many reasons) but as Paul says they are uncoupled from any underlying model. All they do is create pleasing-to-the-eye smooth curves. See any undergrad book on numerical methods.

(Verhulst) logistic function on the other hand is based indeed on models that crop all up over the place. They correspond to simplifications in SIR models etc.

I tried to find models from the confident Swedes. i could only find this 'note' (not peer-reviewed I am sure, the authors even don't believe what they are writing .. section V).

https://arxiv.org/abs/2004.01575
Thy reduce the ODEs to Woods-Saxon forrn (nuclear physics analogy...). This confounds the material and is non-standard .. just use/learn the Verhulst model and it's a starting point, indeed. Why drag physics analogies into the discussion??

// This 3-page, 4-author note has several typos, is incomplete and unresearched if you look at the references.

Very unconvincing.