MEM spectral analysis for predicting influenza epidemics in Japan

Abstract

Objectives The prediction of influenza epidemics has long been the focus of attention in epidemiology and mathematical biology. In this study, we tested whether time series analysis was useful for predicting the incidence of influenza in Japan. Methods The method of time series analysis we used consists of spectral analysis based on the maximum entropy method (MEM) in the frequency domain and the nonlinear least squares method in the time domain. Using this time series analysis, we analyzed the incidence data of influenza in Japan from January 1948 to December 1998; these data are unique in that they covered the periods of pandemics in Japan in 1957, 1968, and 1977. Results On the basis of the MEM spectral analysis, we identified the periodic modes explaining the underlying variations of the incidence data. The optimum least squares fitting (LSF) curve calculated with the periodic modes reproduced the underlying variation of the incidence data. An extension of the LSF curve could be used to predict the incidence of influenza quantitatively. Conclusions Our study suggested that MEM spectral analysis would allow us to model temporal variations of influenza epidemics with multiple periodic modes much more effectively than by using the method of conventional time series analysis, which has been used previously to investigate the behavior of temporal variations in influenza data.

Spectral analysis based on fast Fourier transformation (FFT) of surveillance data: the case of scarlet fever in China

“…In equation (1), the trend component, describing the long-term changes in data, is the polynomial function of time t. The periodic component is referred to as a function with known period, and the random noise component represents random errors, which is commonly treated as Gaussian white noise [15].…”

“…This is inappropriate, especially when the seasonal patterns remain elusive. Second, some analyses focus on the separate estimation method [15], which, in fact, consists of two separate steps: (1) to obtain the frequency parameter by means of the maximum entropy method (MEM); and (2) to utilize least squares fitting (LSF) to estimate the incidence curve. Such methods are simple, but their efficiency is yet to be demonstrated [16].…”

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“…Here,ŷ t denotes the morbidity approximation for the period t; α j and β j are the parameters; the polynomial degree of ν is usually equal to one; and θ j is a linear function of t that can be chosen using spectral analysis [36,70]. The most used function is θ j = 2πjt/T , where T is the number of periods per season, for instance, 12 months or 52 weeks.…”

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