A Density Query

One factor relevant to different rates of Covid deaths in different countries is population density. People often talk about herd immunity as if it required the same percentage of immune people everywhere, but that obviously is not true. In a society where the average individual only encounters someone else every three months, herd immunity starts at zero percent immune. The more people interact, the higher the fraction that must be immune in order that each infected person will, on average, pass the disease on to fewer than one more.

Frequency of interaction depends in part on population density, but not the density calculated by dividing population by area. Adding a million square miles with nobody living there to a country sharply reduces the average population density defined in that way but has no effect on the average density experienced by an individual. What the usual definition is measuring is  density per acre averaged over acres. What we want is the density averaged over people, giving heavier weight to acres that have more people on them. That difference is the reason that people in a country like the U.S., large parts of which are nearly empty, tend to greatly overestimate how crowded it is — almost all the places they observe are places with people in them.

Does anyone know of a source for the form of population density I want? It might turn out that some countries had a much higher density relative to others than the conventional figure implies.

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