As a first motivating example, according to an Oxford CEBM map [even] Sweden has more deaths per capita from Covid-19 (217 deaths/mil.pop.) than the US as a whole (166 deaths/mil.p.) On top of that, according to Wikipedia the US has higher population density (34 per km2) than Sweden (23 per km2). So in that view, Sweden is doing "doubly worse" worse (320 = 217 * 34/23) than the US.
As another data point, Spain for example has 496 deaths/mil.pop. but their population density is 93 per km2. So that makes Spain seen closer to the US--their number would roughly be a third (181 = 496 * 34/93) if (crudely) adjusted by population density to compared to the US.
For Italy, their population density is twice that of Spain (200 per km2) and their deaths per mil.pop. (441) are even less than Spain's. So that makes Italy look good in comparison to Spain in this view. Even compared to the US, Italy fares better (75 = 441 * 34/200) in this perspective.
My calculations are fairly crude adjustments though, ignoring the fact that within countries (esp. US or Sweden) there are large internal variations in population density. So are there some studies/maps that plot the local Covid-19 death rate relative to the local population density (worldwide)? (Of course one needs to do some clustering to produce such maps, so I'm leaving fairly open-ended what "local" means.)
As more motivation for this q, I found a paper on the 1918-1919 flu deaths (per capita) vs population density (in the US):
Investigations of possible links between population density and the propagation and magnitude of epidemics have so far proved inconclusive. There are three possible reasons (i) A lack of focus on appropriate density intervals. (ii) For the density to be a meaningful variable the population must be distributed as uniformly as possible. If an area has towns and cities where a majority of the population is concentrated its average density is meaningless. [...] Here we show that when these requirements are properly accounted for, the size of epidemics is indeed closely connected with the population density.
Relationship between population density d and the size µ of the influenza epidemic of September-December 1918. In the graph m means million. The data are for Indiana, Kansas and the city of Philadelphia in Pennsylvania. Influenza and pneumonia deaths are counted together. It can be seen that the relationship between population density holds only on a broad density scale. Inside of the three groups of data points the background fluctuations are strong enough to override the power law. The regression reads (the confidence interval is for a confidence probability of 0.95): µ = Cdα, α = 0.22 ± 0.08, C = 3.5. Source: Bureau of the Census (1920).
So yeah, the correction for pop density should probably be on a power law, not (linearly) how I've done it in the first part of my question. Doing this (power law correction) instead however, would "disadvantage" the low-density areas/countries even more than how I've done it in the first half of my question!
So, to repeat my question: are there any published models/maps of this kind (adjusting the death rate for population density) for Covid-19?