How not to map the covid-19 pandemic

As my university — like so many others — is using Spring Break to transition from face-to-face courses to putting all online for the rest of the Spring Semester, I decided to check the CDC’s new website for information about how many cases have been reported in Maine and have tested positively. I found this wonderful graphic, which is testament to the fundamental problem of mapping absolute values in a choropleth:

CDC map of covid-19 cases in the USA, as of noon EST on 11 March 2020; click on map to go to site.

The issue is false impression: California, Washington, and New York all stand out as having over 100 confirmed cases; they are large states and have large populations, so the visual impact is intensified. But what is the density of the disease? That is, what might (approximately, of course, given all the laxity surrounding this data) the probability be of encountering an infected person?

If the CDC mapped positive tests per head of population or even per square mile of each state, then the viewer will not be presented with such a strongly misleading impression. Or map the data on a cartogram of states sized by their populations.

(Of course, if the CDC could provide the information by counties, then a cartogram would be required to eb able to discriminate hotspots in small urban counties.)