Geographic Spread of Influenza under the Influence of Community Population Size, Which Differed from That of Measles and Rubella

Abstract

The influenza season is defined as the period from week 36 of the year to week 20 of the subsequent year in this report. The population size of prefectures (x) and number of patients per prefecture (y) were initially uncorrelated, but a correlation developed as the season advanced. The correlation with correlation coefficient >0.7 emerged increasingly earlier over time; it developed in week 5 of the subsequent year in 2001/2002, but in week 47 of the same year in 2014/2015. Once x and y were correlated, plots of y on the vertical axis against x on the horizontal axis resulted in a straight line, y = Cx^s, where s was the slope of the plot and C was a constant. The slope was high (s>1) initially, but decreased (s<1) later, indicating that influenza first spread to populated prefectures and then nationwide, involving less populated prefectures. This spread pattern was the same for the seasonal influenza and AH1pdm2009, although the progression of the latter was much faster. For measles and rubella epidemics, the number of patients per prefecture was proportional to the square of the population size from the start to the end of the season.