Coxsackie B (CVB) enterovirus serotypes have recently attracted attention as a cause of type 1 diabetes, which has a high incidence high among children in European countries [1,2]. The estimated increase in annual incidence of type 1 diabetes in Europe was 3.9% (95% CI 3.6%, 4.2%) from 1989 to 2003; worldwide, the estimated annual increase was 2.8% (95% CI 2.4%, 3.2%) from 1990 to 1999 [3].
Examining the periodic structure of CVB serotype surveillance data is essential for predicting the epidemic of type 1 diabetes. Some researchers have reported cyclical variations in yearly incidence rates of type 1 diabetes—4-year intervals in the Yorkshire region in England from 1978 to1990 [4], a 6-year cyclical pattern in a neighboring area of northeast England from 1990 to 2007 [5], a sinusoidal cycle with peaks every 5 years in Western Australia from 1985 to 2010 [6], and a 5.33-year periodicity in Poland during the period 1989-2012 [7]. More recently, to help clarify recent trends in European incidence rates, European Diabetes registry data were analyzed from over 84,000 children in 26 European centers representing 22 countries from 1989-2013, with separate estimates of incidence rate increases derived in five subperiods [3].
To date, no studies have examined whether surveillance data for CVB serotypes show similar cycles as those in type 1 diabetes incidence data, likely because studies investigating publicly available CVB serotype surveillance data for Europe are lacking. On the other hand, in Japan, CVB serotype surveillance data has been collected for 20 years [8]. The purpose of this study was to investigate the periodic structure of Japanese CVB serotype surveillance data of using time-series analysis based on the maximum entropy method (MEM) in the frequency domain and the least squares method (LSM) in the time domain [9, 10].
CVB Serotype Surveillance
Monthly surveillance data of CVB serotypes (CVB1, CVB2, CVB3, CVB4, and CVB5) from January 2000 to December 2018 (228 data points) were analyzed. The number of specimens that test positive for pathogens and viruses, including CVB serotypes, are regularly reported to the National Institute of Infectious Disease Surveillance Center (Tokyo, Japan). These data are published in the monthly periodical Infectious Agents Surveillance Report [11].
Monthly surveillance data of CVB serotype from January 2000 to December 2018 are shown in Figure 1. Therein, all incidence data show a yearly cycle with large epidemics every few years, for example, CVB1 (Figure 1a) in 2004 and 2011 and CVB2 (Figure 1c) in 2005 and 2009.
Periodicity of the Surveillance Data
Power spectral densities (PSDs) obtained with the MEM spectral analysis (Additional file 1) for the data in Figure 1 are shown in Figure 2. In each plot— CVB1 (Figure 2a), CVB2 (Figure 2b), CVB3 (Figure 2c), CVB4 (Figure 2d), and CVB5 (Figure 2e)—prominent spectral peaks were observed at f = 1.0 [units (1/year)], corresponding to the 1-year cycle, that is, the seasonal cycle. In the low-frequency range, f < 1.0, reflecting oscillations longer than the 1-year cycle, several prominent spectral peaks were observed. In each power spectral density plot, the dominant spectral peak was observed during an approximately 3- to 5-year period. For each serotype, five dominant spectral frequency mode peaks with corresponding periods and powers are listed in Table 1.
With the five periodic modes that were clearly observed in each PSD (Table 1), the least squares fitting (LSF) curve (Additional file 2) for each serotype was calculated. Each LSF curve thus obtained is presented in Figure 1
Each LSF curve reproduced the original data well (Figure 1), which confirmed the periods from MEM spectral analysis (Figure 2, Table 1) were accurate. Pearson correlations between the original data and the LSF curves—ρ = 0.96, ρ = 0.60, ρ = 0.90, ρ = 0.88, and ρ = 0.67 for CVB1, CVB2, CVB3, CVB4 and CVB5, respectively—further demonstrated a good fit.