Unflattening in Washington County (Utah)

Uh oh.

Cases are going up at a somewhat more disturbing rate in Washington county, Utah (St. George metropolitan area). I'm going by memory, but I believe about a quarter of SUU students are from there, so this should be of special interest.*

I'm still up here in Iron county, and the data is not showing the same behavior here. Possibly, this is because infection rates here are about half of what they are in Washington county.

Utah has been opening up for a little over 2 weeks. This is due to widespread perception that we have "flattened the curve".

I sense that more people use that phrase than really understand what it means. That is, a flattening of a curve on some time series chart with a log scale, like this one:

The log scale is important; "flattening" is defined with respect to logged data only. It corresponds to "growing more slowly" (part of the reason data scientists like logs is that the slope on a graph like this is proportional to a growth rate). The base for the logs is not important for seeing flattening. But, the base is important for some other things you might want to do with this graph. I prefer to use 2 as my base (most sources online use 10 as their base, which to me is inexplicable, and smacks of innumeracy).

What we see for Washington county is that the epidemic, while small, was growing quickly in March. While the world is new to shelter in place orders, the general belief is that they take a couple of weeks to produce a difference. We see that here: April was a month of flattening for Washington county. But May ... not so much.

Another way to look at this is how long it takes a variable to double (we could do other multiples, but people are most comfortable with doubling). This is where the usefulness of base 2 logs comes in: doubling on a chart of base 2 logs corresponds to going up by one. And, for any two days where that logged data goes up by 1, we can just count the days off along the horizontal axis. Even better, we can chart that too:

 

This chart "looks backwards": from a date on the horizontal axis, how many days do we have to count backwards before we get to half as many cases. The quick drop to low numbers in March shows the outbreak getting a foothold in the county. The steady increase through April shows the effectiveness of shelter in place orders. But things have gotten worse in May. The latest date shown here is May 19th, and Washington county's cases have doubled since May 9th.

The same thing has happened with deaths. There have only been four COVID-19 deaths in Washington county so far. Initially, they doubled from one to two in 28 days. They doubled again from two to four in 25 days.

Keep in mind that what is shown here is positive test results. Those are not a great measure of the status of an outbreak, but this is the best one anyone has got. Cases are positive test results. They will go up when there are more infections, but only when more tests are done. They will also go up when infections are not increasing if more tests are done. After considerable delay, by early April the U.S. was testing more than other countries, so that second reason is probably not a concern anymore.

* County level data on cases and deaths is now being tabulated by The New York Times, and is freely available for download from GitHub.
† I do have people from outside my classes read this blog, and in particular from outside of Utah. Washington is a fairly common name for counties, so I specified that in the title.