Rotavirus Seasonality: An Application of Singular Spectrum Analysis and Polyharmonic Modeling

Abstract

The dynamics of many viral infections, including rotaviral infections (RIs), are known to have a complex non-linear, non-stationary structure with strong seasonality indicative of virus and host sensitivity to environmental conditions. However, analytical tools suitable for the identification of seasonal peaks are limited. We introduced a two-step procedure to determine seasonal patterns in RI and examined the relationship between daily rates of rotaviral infection and ambient temperature in cold climates in three Russian cities: Chelyabinsk, Yekaterinburg, and Barnaul from 2005 to 2011. We described the structure of temporal variations using a new class of singular spectral analysis (SSA) models based on the “Caterpillar” algorithm. We then fitted Poisson polyharmonic regression (PPHR) models and examined the relationship between daily RI rates and ambient temperature. In SSA models, RI rates reached their seasonal peaks around 24 February, 5 March, and 12 March (i.e., the 55.17 ± 3.21, 64.17 ± 5.12, and 71.11 ± 7.48 day of the year) in Chelyabinsk, Yekaterinburg, and Barnaul, respectively. Yet, in all three cities, the minimum temperature was observed, on average, to be on 15 January, which translates to a lag between the peak in disease incidence and time of temperature minimum of 38–40 days for Chelyabinsk, 45–49 days in Yekaterinburg, and 56–59 days in Barnaul. The proposed approach takes advantage of an accurate description of the time series data offered by the SSA-model coupled with a straightforward interpretation of the PPHR model. By better tailoring analytical methodology to estimate seasonal features and understand the relationships between infection and environmental conditions, regional and global disease forecasting can be further improved.

An analecta of visualizations for foodborne illness trends and seasonality

“…In the proposed approach, we present the amplitude as the ratio of seasonal peak to seasonal median, which offers robust estimation even for rare or highly sporadic infections. These features are not available when traditional models, like Auto-Regressive Integrated Moving Average (ARIMA), are applied 56 . Measures of uncertainty enable formal testing and comparisons across diseases in the same location or locations for the same disease.…”

Assessing Seasonality Variation with Harmonic Regression: Accommodations for Sharp Peaks

“…Though three types of distributions: Gaussian, Poisson, and negative binomial assumed, most often Poisson harmonic regression is applied to accommodate the skewed nature of counts. The main drawback of harmonic regression is that it assumes a symmetrical nature of a harmonic process with the same rate of an increase and decrease in disease incidence from nadir to peak and vice versa [26]. Thus, by assuming a symmetric well-defined periodic structure, traditional harmonic models may not be ideal to capture the departures from stable oscillations [27].…”

“…The typical periodic oscillations well defined in epidemiology occurred on a weekly, monthly, or quarterly basis and therefore these cycles are observed within a year. We recognize the limitation in using monthly values, which offer a coarser estimate than could be offered by refined time units, like days or weeks [26]. In order to improve the descriptive power of the regression models adapted to time series of counts to detect these cycles, it would be valuable to examine how the degree of temporal aggregation affect the accuracy and precision.…”

“…Thus, the interest of a study might be to identify factors that influenced a trend of a disease. Such factors could be represented by environmental, clinical, or demographic variables [7][8][9][10]26,27,31,37,38]. For example, in investigating the factors associated with seasonal peaks of cholera various environmental, climatic, and meteorological factors demonstrated potential links and provide an insight to underlying mechanisms [4].…”

“…We also assumed that the strong autocorrelation in the outcome time series is not of major concern after controlling for seasonality and trend patterns [39]. Yet, such an assumption should be further tested along with the assumption of a true annual period [26].…”