Department of Hygiene, Sapporo Medical University School of Medicine, S-1, W-17, Chuo-ku, Sapporo 060-8556, Japan.
Environ Health Prev Med. 2012 Mar;17(2):98-108. doi: 10.1007/s12199-011-0223-0. Epub 2011 Jun 7.
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.
流感的预测一直是流行病学和数学生物学关注的焦点。本研究旨在检验时间序列分析是否有助于预测日本流感的发病率。
我们使用的时间序列分析方法包括基于最大熵法（MEM）的频域谱分析和时域非线性最小二乘法。利用该时间序列分析，我们分析了 1948 年 1 月至 1998 年 12 月期间日本流感的发病率数据；这些数据的独特之处在于，它们涵盖了日本 1957 年、1968 年和 1977 年的流感大流行时期。
基于 MEM 谱分析，我们确定了解释发病率数据基本变化的周期性模式。利用这些周期性模式计算的最优最小二乘拟合（LSF）曲线再现了发病率数据的基本变化。LSF 曲线的扩展可用于定量预测流感的发病率。
我们的研究表明，MEM 谱分析比以前用于研究流感数据时间变化行为的传统时间序列分析方法更有效地模拟流感流行的时间变化，该方法可以使用多个周期性模式。
