I guess it depends on what you want to do. If you're trying to make sense of a given countries response, (cases) / (population of administrative region) seems l

I guess it depends on what you want to do. If you're trying to make sense of a given countries response, (cases) / (population of administrative region) seems like a decent metric. Also since policy tends to follow administrative lines it's a decent (but extremely noisy) metric to see what policies are working. What do you want to learn from (cases) / (people in infected area)? The denominator seems difficult to define since it's not scale invariant. If you defined an "infected area" as being within 1 km of an infected person, for example, you'd get a very different answer from if you defined infected area as 10 km from an infected person. In the limiting cases where you define infected area with very fine or very course granularity, you get an infection rate of 1.