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The size distribution of a local infection cluster (LIC), a group of infections reported from the same prefecture without interruption in successive weeks, was scale-free for infections that are transmitted from person-to-person (e.g., measles, rubella, syphilis, and HIV/AIDS). For infections that do not spread from person-to-person, the distribution was entirely random. The size distribution for measles, rubella, syphilis, and HIV/AIDS could be simulated successfully by random coin tossing with probabilities that were higher for highly populated prefectures. The size distribution of the population in large municipalities (&gt;120,000), as well as that of LICs, was found to be scale free. As the number of patients per prefecture was correlated with the equation P = kN m , where m was 1.38 for syphilis, 1.63 for HIV/AIDS, and 2 for measles or rubella, the frequency distribution of N 1.38 , N 1.63 , and N 2 , where N was population of municipalities, was compared with the frequency distributions of LIC sizes of syphilis, HIV/AIDS, measles, and rubella. The frequency distribution of LICs, particularly those of measles and rubella during the years when the epidemic was more severe, was close to the frequency distribution of N m . The analysis suggested that LICs were products of stochastic events under the influence of municipality population size.

japanese journal of infectious diseases

Scale-Free Distribution of Local Infection Clusters of Measles, Rubella, Syphilis, and HIV/AIDS: Correlation with Scale-Free Distribution of Municipality Population by Size