Seasonality of Influenza: An Investigation Using Time Series, Spectral Analysis & Epidemiological Models

Abstract

Influenza is an infectious disease. Its seasonality is commonly modeled focusing on the yearly cycle. The log transform of pneumonia and influenza mortality data from the United States from 1910 to 2015 showed an approximate 30 year recurring pattern. The data were analyzed in the time domain and then in the frequency domain using the multitaper spectrum estimation method. Significant frequencies were identified using the F-test and confirmed by the presence of distinct square peaks in the spectrum plot. This monthly sampled data identified long-term trends at 136 year, 14 year, 11 year and 7.5 year periods as well as high frequencies of 2, 3, 4 and 5 c/y. These intriguing results led to the analysis of influenza incidence data from the United States, United Kingdom, Australia and Japan. Simulated data was generated from a susceptible-infected epidemiological model with the contact rate of influenza transmission set to a one-year period. It was also modified to include multiple periodic terms that were identified as significant in the collected datasets. After comparing the spectral results of the collected and simulated data, similarities were easier to notice and interpret. Spectral analysis identifies frequencies that contribute to the variations in the data. These frequencies could have individual biological significance and/or aid in the attempt to represent the data that are non-sinusoidal by summing their sinusoids. The high frequencies are most likely harmonics of the yearly cycle, where 2, 8 and 9 c/y are recommended to be considered in inclusion in multi-term periodic models. Simulations presented the opportunity to compare the effect of sampling rates and data length on the spectral results. It is recommended to use weekly sampled data of at least 30 years. The results from investigating influenza morbidity and mortality data in the frequency domain aid to better understand the patterns of the data, which can be used to improve forecasting of influenza data.