It has been known since the 1950s that when a community’s size is below a certain threshold, measles does not persist consistently through time, it will have “fade-outs” – Bartlett looked at this in the U.S. and England, and found that threshold to be in the range of 250,000 to 300,000. That, however, does not refer to population density (which is what we would use in ecology when looking at density dependent effects), but total population of the given community, e.g., New York City, or Akron, or Philadelphia.
Given that members of these communities are centered around a city, for work, for leisure, for administrative needs (e.g, voter registration, or DMV), this is a very reasonable number to use, likely moreso than population density, as it informs the number of interacting individuals who may come in contact with each other and spread transmissible disease.
http://www.jstor.org/discover/10.2307/2343186?sid=21105263993991&uid=70&uid=4&uid=2&uid=2129
The Critical Community Size for Measles in the United States
M. S. Bartlett
Journal of the Royal Statistical Society. Series A (General)
Vol. 123, No. 1 (1960), pp. 37-44
Urbanization and humidity shape the intensity of influenza epidemics in U.S. cities. Benjamin D. Dalziel, Stephen Kissler, Julia R. Gog, Cecile Viboud, Ottar N. Bjørnstad, C. Jessica E. Metcalf, Bryan T. Grenfell. Science Oct 2018 : 75-79
Public Health News and Views 