It seems fairly obvious that density should correlate with how fast a virus spreads. Comparing across countries or even states is difficult due to time of introduction as well as many other variables. This should be less of a problem (but certainly not zero problem) for a study of of cases by county within a single state. Therefore I looked at the relationship between density and cases. Keep in mind this is an ongoing pandemic so time of introduction will still make a difference, and for that matter there is no effort to control for other variables (e.g., difference in testing frequency by county.) Both axes are log 10 mostly to group points together. As you can see from the R^2 there's quite a close association.
The next and less obvious question is, if viral load (total number of viruses an infected person was exposed to) correlates with illness severity, you would expect that density would also correlate with deaths. There are even more variables that come into play with deaths - age and health of the population which definitely differs, as well as access to medical care and ICU beds. So I did the same thing for deaths; I'm not showing it since I found an R^2 of only 0.0845. I predict that a month from now that R^2 will be higher.
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