Population Dependency of Measles, Syphilis, and Amebiasis in Japan and Community Evolution.

The population dependency of measles, syphilis, and amebiasis was expressed as P = kNm, where P, N, and m were number of patients, population size, and a constant (～2 for measles, and 1.3～1.4 for syphilis and amebiasis), respectively. The population size dependency emerged only when conditions other than population size, such as infant mortality, hygienic condition, vaccination practices, and others, improved to the same level in all the prefectures in Japan. The formation of prefectures and municipalities was well simulated by the random coin toss assuming that people are attracted to a community with a probability proportional to the number of the residents to the 1.3rd power. When the number of inflow population was plotted against the number of the resident population in a prefecture, or when the number of coins that were added in a round was plotted against the number of coins that were present before the coin toss, the plots fell on a straight line with the slope ～1.3, which was almost the same as the slope obtained when the number of cases of syphilis or amebiasis was plotted against the population size.