Seasonality is a defining feature of many epidemiological time series, reflecting recurring patterns over time. Accurate characterization of these patterns is essential for influenza surveillance, forecasting, and public health planning.This study examines influenza incidence in Wisconsin using laboratory-confirmed weekly case data from 2021–2025 provided by the CDC. We compare four approaches for modeling seasonal time-series data: seasonal dummy variables, Fourier harmonic regression, Seasonal ARIMA models, and generalized additive models (GAMs) with spline-based smoothers. While recent studies have applied GAMs to assess meteorological effects, few have used this flexible approach to directly model the underlying seasonal structure of respiratory infection data.Results show that the spline-based GAM consistently outperforms alternative methods. It captures shifting peak timing, asymmetric seasonal curves, and multiple inflection points, the features that more rigid approaches cannot fully represent. No evidence of overfitting was observed. Findings also suggest increased variability in post-COVID influenza seasonality in Wisconsin, highlighting the need for adaptive, data-driven models.
