Scale-Free Distribution of Local Infection Cluster Sizes of Measles, Rubella, Syphilis and HIV/AIDS: Correlation with Size Distribution of Municipality Population That Was Also Scale-Free

Abstract

The size distribution of the local infection cluster (LIC), a group of patients 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 never 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 the large municipalities (>120,000) as well as that of LICs were found scale free. As the number of patients per prefecture was correlated with an 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^1.6 and N², where N was population of municipalities, were 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 large epidemic years, was close to the frequency distribution of N^m. The analysis suggested that LICs were products of stochastic events under the influence of the municipality population size.