Study on Chaotic Characteristics of Incidence Data of Measles

Abstract

In this paper, the chaotic characteristics of time series data of monthly number reported cases of measles in New York City from January 1928 to December 1963 were investigated using the computing program “MemCalc”. Power spectral densities (PSDs) were calculated for the measles data, two types of time series numerically calculated from the SEIR epidemic model (the chaotic and periodic time series) and the noisy time series. Exponential characteristics were observed in the PSDs for the measles data and the chaotic and periodic time series, but not observed in the PSDs for the noisy time series. For the measles data and the chaotic time series, the PSDs exhibit the broad continuous peaks peculiar to the chaotic state. The behavior of the three-dimensional spectral array obtained from segment time series analysis is distinguishable from the cases of the periodic and noisy time series. It was concluded that the dynamics of the measles data is chaotic. The present method was used to extract the chaotic characteristics from measles data having a short time period.