Actually, using Excel to fit curves was good enough to get my PhD and publish on my research. So I'm pretty comfortable with the program and the calculations. What I am looking for, actually, is any sign that the growth is slowing, which would be reflected in the graphs by a decreased R squared value on the trendline. At that point, it would be appropriate to start deriving the exponential equation for this disease--although I'm not going to do that, since I won't be publishing. As for the extrapolations, I am completely comfortable with making them, since, like any exponential growth function, the rate of growth follows a very predictable trajectory.
This is not even comparable to what the "climate folks" do. They have taken a faulty premise--that carbon dioxide's wide band of fluorescence in the infra red frequencies equates to an increase in the energy content of the atmosphere--and extrapolated all kinds of stuff from that. Garbage in, garbage out. The fields of microbiology, epidemiology, etc., have a LOT of data and research to validate the models regarding disease spread.
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.
As I said above, I'm looking for a change in the R squared value, which could mean that the growth of cases is slowing. Sure, determining the actual exponential equation is a bit more complicated than using a polynomial (which I already know from a TON of experience is close to within a few thousands to the actual values calculated by an exponential equation). But it's not necessary, and I don't have the full data set in any case to determine the actual exponential equation. That's because I don't know and no one knows when the increase in new cases will slow.
Good post. The epidemiological term you are looking for is Inflection Point.
Your a PhD in I don’t know what so I cant tell you anything i guess. You clearly weren’t a PhD in math or engineering. Only the start of the cycle could be described as close to an exponential curve. The growth AND decay of the cycle is not an exponential, it going to be more sinusoidal, which is described by Fourier better than polynomial.
An exponential fit is one of many tools in a tool box. If you had studied math, statistics to any degree you would be looking at ALL the other tools in the box knowing that at some point this is no longer exponential.
It’s likely this would be fit by a first or second order Fourier fit or first order Fourier polynomial. I’ve done my part to make you aware. Carry on PhD