Population Size Dependency of Measles Epidemic That Was Scalable from Japanese Prefectures to European Countries.

The relationship between the number of measles patients (y) and the population size (x) was expressed by the equation y=axs , where a is a constant and s the slope of the plot; s was 2.04-2.17 for prefectures in Japan, i.e., the number of patients was proportional to the square of the population size of the prefecture. For European countries that joined the European Union (EU) no later than 2009, the slope was 1.43-1.87. The population dependency of measles found among prefectures in Japan was thus scalable to European countries. This was surprising because, unlike Japan, the population densities of EU countries were not uniform and not proportional to the population size. The population size dependency was not observed among Western Pacific and South-East Asian countries probably due to confounding from interacting socioeconomic factors. The correlation between measles incidence and birth rate, infant mortality or gross domestic product per capita was almost insignificant. The size distribution of local infection clusters (LICs) of measles and rubella in Japan followed a power law. For measles, although the population dependency remained unchanged after "elimination," there were changes in the Zipf-type plots of LIC sizes. After "elimination," LICs linked to importation-related outbreaks in less populated prefectures emerged as the top-ranked LICs.