Detecting changepoints in dynamical systems: Modeling time-varying transmission of seasonal influenza

Seasonal influenza epidemics exhibit complex transmission dynamics influenced by time-varying extrinsic factors such as social behavior and seasonal effects. Estimating changes in transmission rates is critical to enable accurate forecasting of the epidemic curve. This study presents a framework for detecting changepoints in the transmission parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:msub> </mml:math> ), applied as a piecewise constant function within a deterministic compartmental model. Using hospitalized case data from four recent influenza A seasons in Ireland (2019/2020 and 2022–2025), we applied iterated filtering and kernel density estimation to identify season-specific and cross-seasonal changepoint structures. The algorithm integrates stochastic search, local perturbation, and resampling to infer the most plausible changepoint configurations. Results reveal consistent changepoint patterns across seasons, particularly during periods of increased social mixing, such as the December holiday period. A universal changepoint model was also developed, enabling medium-term forecasting and scenario planning. This approach offers a robust method for capturing abrupt shifts in transmission and may be applicable to other dynamical systems.