A constant 2nd-derivative means quadratic growth, not exponential.
I'm bit confused by the graphs, because they show the 2nd-derivative going to 0. But to stop this thing, we actually need to decelerate, eg going negative on the 2nd-derivative.
I'm bit confused by the graphs, because they show the 2nd-derivative going to 0. But to stop this thing, we actually need to decelerate, eg going negative on the 2nd-derivative.
Edit: Now that I think about this some more, you're right. There has to be a decrease in the daily cases, which implies a negative 2nd-derivative. They mention "relative 2nd-derivative." It seems to be defined in the paper in a way that leaves me more confused:
> Daily fatality rates from the included countries were then used to calculate estimates of the relative second derivative of total deaths, N, 1/N d²N/dt², for a period of at least ten days.
Does this mean they are taking the second derivative of the reciprocal of the cumulative deaths?
A constant relative second derivative of total deaths is what they are talking about, meaning that they are flattening the 2nd derivative of the exponential by dividing by the exponential, making it constant.
Of course, this is all numerical methods, not analytical methods, so it doesn’t necessarily make pure analytical sense that they are even talking about an exponential.
You are treating the curve of daily deaths as the thing to be differentiated. They are treating the curve of total deaths as the thing to be differentiated.
While the curve of daily deaths certainly would have a negative acceleration, the curve of total deaths is monotonically non-decreasing and therefore the second derivative is always positive but trending towards zero.
Like I mentioned above, the only way for total deaths to decrease (making the function not monotonically increasing and therefore capable of having a negative acceleration) would be through errors of accounting.