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

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Novosibirsk State Technical University, Novosibirsk 630073, Russia

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Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia

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State Research Center for Virology and Biotechnology “Vector”, Koltsovo, Novosibirsk Region 630559, Russia

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Friedman School of Nutrition Science and Policy, Tufts University, Boston, MA 02111, USA

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Author to whom correspondence should be addressed.

Received: 23 August 2019 / Revised: 1 November 2019 / Accepted: 1 November 2019 / Published: 6 November 2019

(This article belongs to the Special Issue Infectious Disease Modeling in the Era of Complex Data)

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.