Originally Posted by
Winemaker
For what is worth, was mucking about with the Chinese numbers and came up with this:
The concern with all of the information provided to date is that as you indicate, there is a cubic fit to the data.... with a fair match, (R2 in high .99.... ). This is a virus, which in the absence of limiting constraints has an exponential function for case growth. The curve for a quadratic looks like an exponential function over the first few values of x, thereafter they diverge, quite rapidly. A cubic function, (your example fit of abX^3+cdx^2+k) will have two curves combined, and may approximate an exponential function, at early values of x, and then will diverge as well from exponential functions.
So far, the provided data doesn't fit an exponential growth, and that is curious. Either there are constraints to the growth that do a remarkable job of matching a quadratic or cubic function, (at least over part of the growth in numbers) or the data ain't the full monty. Being of generous mind, I choose to assume that there are other constraints involved, such as interventions etc, that are altering the course of the cases. That isn't necessarily being naiive, there is a fair chance that the breakout from Hubei gave anomalous growth rates in cases, and intervention by various countries to control the spread. If the numbers have however been back driven, then that will become identifiable in due course assuming that the data of the rest of the world can maintain integrity.
Fatalities in this outbreak have taken some time to occur, actually much longer than was assumed first up. WHO/CDC are not reporting that time at present, but the cases that have been looked at show a progression that takes between 7 days and 14 days from contagion to death. That increases the mis-match in the CFR methodology, however, the reported fatalities are not following a consistent progression compared to reported cases for the early to mid January data (slip fatalities at the end of January forward by 10 days, and they are almost equivalent to the number of cases reported at the earlier time, when the fatal cases were exposed to the virus, yet 10 days later in the data, this is not the case).