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Environ Health Prev Med (2012) 17:98108 DOI 10.1007/s12199-011-0223-0
REGULAR ARTICLE
MEM spectral analysis for predicting inuenza epidemics in Japan
Ayako Sumi Ken-ichi Kamo
Received: 30 September 2010 / Accepted: 15 May 2011 / Published online: 7 June 2011 The Japanese Society for Hygiene 2011
AbstractObjectives The prediction of inuenza 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 inuenza 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 inuenza 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 identied the periodic modes explaining the underlying variations of the incidence data. The optimum least squares tting (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 inuenza quantitatively.
Conclusions Our study suggested that MEM spectral analysis would allow us to model temporal variations of inuenza 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 inuenza data.
Keywords Inuenza Prediction analysis
Time series analysis Surveillance Epidemiology
Introduction
For preventing and predicting inuenza epidemics, it is necessary to investigate temporal variations of the disease morbidity data in detail [15]. To elucidate temporal variational structures in the morbidity data of inuenza, many studies have been carried out by using conventional time series analysis [612], such as a Gaussian random process for the modeling of inuenza epidemics [12] and an autoregressive model (AR) including a seasonal autoregressive-integrated moving average model [10].
On the other hand, recently, researchers have tried to interpret the behavior of temporal variations in the morbidity of inuenza in terms of nonlinear dynamics which causes multiple periodic structures with characteristic...