In this case, the data is very good for extrapolation. Disease outbreaks always follow a classical growth curve. Until the outbreak starts to pass, we will continue to see this kind of growth.
The problem with the “climate change” modeling is that it is based on incorrect assumptions. The rate of spread of disease is a topic that is very well studied.
That is exactly the mistake climate folks make. You can’t extrapolate. As soon as the curve breaks it’s a different equation, a different model. You can only use interpolation equations safely within the data set. As soon as you go beyond what you know historically, it will diverge, unless you have a full cycle of data. You don’t have a full cycle for this virus and this population set. No one does. You think you have a good model because excel can fit a set of data to a curve? That is just incorrect.
The only thing I can give you is that there is a good chance that tomorrow will be close to today. But your second order fit only goes one direction - up. You will need a much more complex equation, probably something that includes sinusoidal terms as well as a polynomial, to fit to to all the data once this thing has actually gone full cycle. Then you have a model that might represent the future, assuming nothing changes. But things always change. So it’s still best guess.
And math is math - as long as you know the parameters and conditions.