So, assuming 3 areas 1,000 square miles with 2,000 people, 100 square miles with 4,000 people and 10 square miles with 8,000 people you do : (2,000^2/1,000 + 4,000^2/100 + 8,000^2/10) / (2,000 + 4,000 + 8,000) = 468.8 people per square mile, not (2,000 + 4,000 + 8,000) / (1,000 + 100 + 10) = 12.6 people per square mile.
The reason is adding a huge area that nobody lived in (ex: 1 person across 1 million square miles) doesn’t change the calculation. (1^2/1,000,000 + 2,000^2/1,000 + 4,000^2/100 + 8,000^2/10) / (1+2,000 + 4,000 + 8,000) = 468.8 people per square mile
Go look at a Google street view of the far ends of Stockholm metro area…
Stockholm’s urban area of 11,000/sq mi across 147.35 sq mi, is comparable to Paris, but it’s inner core 73 sq mi is a much lower density 13,000/sq mi. Even if you assumed all those people lived in a 40 square mile “inner inner” core you still don’t get close to 53,000/sq mi.
Covid was deadlier in urban areas. Compare rural regions, such as the ones bordering Norway and Sweden, and the mortality is pretty much comparable across the border. Slightly on the Swedish side, but well within what can be ascribed to random variability. That doesn't make the border closings look especially effective in retrospect. The virus doesn't care about borders.
We care about the population density of population, not the population density of land. It’s sometimes call the population-weighted density.
Countries should be evaluated based on performance relative to doing nothing not relative to other counties in very different situations. Niger has a median age of 15.4, Italy has a median age of 45.5 they simply have vastly different ratios of the elderly etc.