Huh?

This post explains how to read the weekly growth charts.

I've already gotten good feedback from my first post. To paraphrase, the questions are along the lines of

"This coronavirus-fed fever dream is great, but how do I read and interpret these graphs?"

"This doesn't make any sense. Why are the graphs going down while the case numbers are going up (and up)?"

To answer those questions, let's use the United States COVID-19 case history as an example (data from Worldometers):

Following the example of the popular Financial Times (FT) plots, we start plotting a country's data when the number of cases exceeds 100, which happened in the US on March 3. This accounts for the pandemic reaching different countries or states at different times, and by lining the various countries up at the same starting point, it is easier to compare the trajectories of the virus in those different countries. FT also uses a logarithmic scale, whereby a exponential growth curve (such as unmitigated disease transmission) appears as a straight line that represents the oft-cited R value in the growth models.

As a result of syncing every country to the same starting point, the FT plots allow us to answer two essential questions:

1. How are different countries doing relative to one another in growth rate and total scale?

2. Are the cases in a country leveling off?

To the naked eye, these log plots show a straight line as the virus takes off (pure exponential growth). Then as a country gets the spread under control, the curve will start to fall below the initial exponential growth line and roll off asymptotically to a residual growth rate.

What we are most interested in, however, is how are policy actions affecting the spread. For this analysis it is more useful to plot the changes in the growth than the absolute numbers themselves. Looking at just the US:

The upper (blue) line is the total number of cases in the US. The lower (orange) line indicates the week over week growth, expressed as the number of cases on a given day divided by the number of cases a week prior. Referring back to the table, and using March 10 as an example, the weekly growth is calculated as

N = number of cases on March 10 = 994

M = number of cases on March 3 (1 week prior) = 124

Weekly Growth Rate = N / M = 8.02

Whereas as detecting changes in the absolute numbers is challenging, the week-over-week numbers clearly indicate when the pandemic is getting under control or further out of control.

Specifically, the interpretation of the weekly case growth is as follows:

1. If the weekly ratios graph is flat (horizontal line on the graph), then the country is showing pure exponential growth. In practice this rarely happens because in the early stages the data is noisy and reporting is likely erratic and in the later stages, people are taking steps to slow the growth rate.

2. If the weekly ratios are going down (negative slope on the graph), then some action has taken place to contain the pandemic. However, as long as the ratios are over 1, it means that the number of cases is still growing. Unless data is revised, the weekly ratio should never go below 1.

3. If the weekly ratios are going up (positive slope on the graph), then there is a loss of containment and it is going to be much more difficult for a country to bring it back under control.

Other comments:

1. One nice feature of the weekly ratio graphs is that they normalize out potential differences between countries in their case reporting. (See Verify for a discussion of potential reporting differences.)

2. While the weekly ratios are a measure of change in the growth of cases, they are not strictly a derivative. A topic for a later post.

3. Different graphs serve different purposes. The weekly ratio graphs are useful for assessing policy changes during the early spreading of the pandemic. As the pandemic is contained, and we approach the endgame, it is more useful to look at changes in new cases instead of total cases.