View the derivative?

[snopicek]

Would it be possible to choose to view the derivative of currently drawn curve instead? It could be better visualization of the divergence from the exponential path...

[exclipy]

The line is already showing a derivative so I'm not sure I could interpret what the second derivative would mean.

But on a similar vein, NYT has basically this graph divided by the x axis. See the last two chart at https://www.nytimes.com/interactive/2020/03/27/upshot/coronavirus-new-york-comparison.html

[snopicek]

Consider for example Sweden. Its path diverged slowly from the main highway, but then it returned to the exponential growth. In the second derivative picture, it would be shown only as a little, on the X axis bounded "dent" in otherwise constant function.

[md2perpe]

I came here for the same idea. Plotting the quotient change/total or perhaps exp(change/total) would show the spread rate. This value could be plotted against time, either absolute or since "day 0".

Mathematics: Assuming an exponential growth u(t) = C a^t, the derivative is u'(t) = (ln a) u(t), so u'(t)/u(t) = ln a.

[prestonraab]

I think a value that would show a similar curve, with a more easily understood connection to the real world, is the percent of total cases which were new in the past week. It would still show exponential growth as a constant, and lend itself to calculations of the doubling rate.

[md2perpe]

@prestonraab. That's more or less the same thing.

[aatishb]

The last graph on the NYT article shared by @exclipy is super interesting. Might be worth looking into adding a view like that here. One of the issues with our log-log curve is that the slope doesn't convey the growth rate, instead the height of the curve does. (All exponential growth has the same slope on our log-log curve). So a separate view focusing on growth rate as suggested here makes sense to me.