MEM spectral analysis for predicting influenza epidemics in Japan

Ayako Sumi,Ken-ichi Kamo

doi:10.1007/s12199-011-0223-0

Ayako Sumi, Ken-ichi Kamo

Open Access

https://doi.org/10.1007/s12199-011-0223-0

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Abstract

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. 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. 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. 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.

Highlights

For preventing and predicting influenza epidemics, it is necessary to investigate temporal variations of the disease morbidity data in detail [1,2,3,4,5]
Objectives The prediction of influenza epidemics has long been the focus of attention in epidemiology and mathematical biology
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

Summary

Introduction

For preventing and predicting influenza epidemics, it is necessary to investigate temporal variations of the disease morbidity data in detail [1,2,3,4,5]. To elucidate temporal variational structures in the morbidity data of influenza, many studies have been carried out by using conventional time series analysis [6,7,8,9,10,11,12], such as a Gaussian random process for the modeling of influenza epidemics [12] and an autoregressive model (AR) including a seasonal autoregressive-integrated moving average model [10]. In order to investigate temporal variations in the morbidity of influenza for predicting the disease incidence, it is necessary to establish a new method of time series analysis. The series of analysis in the present study combines spectral analysis based on the maximum entropy method (MEM) in the frequency domain with the nonlinear

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