Time series analysis of incidence data of influenza in Japan

Abstract

Background: Much effort has been expended on interpreting the mechanism of influenza epidemics, so as to better predict them. In addition to the obvious annual cycle of influenza epidemics, longer-term incidence patterns are present. These so-called interepidemic periods have long been a focus of epidemiology. However, there has been less investigation of the interepidemic period of influenza epidemics. In the present study, we used spectral analysis of influenza morbidity records to indentify the interepidemic period of influenza epidemics in Japan.

Methods: We used time series data of the monthly incidence of influenza in Japan from January 1948 through December 1998. To evaluate the incidence data, we conducted maximum entropy method (MEM) spectral analysis, which is useful in investigating the periodicities of shorter time series, such as that of the incidence data used in the present study. We also conducted a segment time series analysis and obtained a 3-dimensional spectral array.

Results: Based on the results of power spectral density (PSD) obtained from MEM spectral analysis, we identified 3 periodic modes as the interepidemic periods of the incidence data. Segment time series analysis revealed that the amount of amplitude of the interepidemic periods increased during the occurrence of influenza pandemics and decreased when vaccine programs were introduced.

Conclusions: The findings suggest that the temporal behavior of the interepidemic periods of influenza epidemics is correlated with the magnitude of cross-reactive immune responses.

Figure 1.. Monthly incidence data for influenza in Japan (1948 to 1998). a. the original data, a′. histogram of the original data, b. enlargement of the original data during 1980–1998, c. log-transformation of the original data (solid line) and the optimum least squares fitting (LSF) curve (dashed line), c′. Maximum entropy method power spectral density of the log-transformed data in the low frequency range (f < 0.2), d. residual data obtained by subtracting the LSF curve from the log-transformed data, and d′. histogram of the residual data.

Figure 2.. Maximum entropy method power spectral density (MEM-PSD) of the residual data in the low frequency range (f < 1.2).

Figure 3.. Three-dimensional spectral array of the residual data. PSD, power spectral density.

Figure 4.. Temporal variation in the power of f_<1 modes (Q_<1).