Comprehensive Spectral Analysis of Time Series Data of Recurrent Epidemics

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Abstract
A comprehensive spectral analysis of data from the surveillance of infectious diseases in Japan on the weekly incidences of measles, chickenpox, mumps and rubella was carried out using a computing program known as “MemCalc.” Each power spectral density (PSD) indicated exponential decay until it leveled off at a limit determined by the accuracy of the present data. Many spectral lines observed in the PSD could be fully assigned using linear combinations of a few fundamental periods. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduced the underlying variation of disease data and an extension of the curve could be used to predict the incidence of the diseases. The effect of mass vaccinations on measles was quantitatively estimated by analyzing the monthly data from Statistics on Communicable Disease. The periodic modes for seasonal oscillations were also estimated. Some discussions including the chaotic dynamics of data on the outbreak of diseases are presented. The method of analysis was confirmed to be a highly effective in elucidating temporal variations of disease data of short data length.