Speaker
Description
Existing established alternative methods for modeling seasonality use sinusoidal forcing functions, flexible splines, etc. In this talk, I outline a novel method for incorporating seasonality into the SIRS model using modular arithmetic. The study proposes a modular arithmetic approach to model seasonal variations in influenza transmission rates, with smooth transitions between them. Unlike sinusoidal models, which struggle with sharp transmission shifts, the modular approach captures abrupt changes linked to school terms and behavioral changes. Statistical methods like periodic splines achieve accuracy but often lack interpretability; the modular framework balances interpretability and data requirements. The study develops this framework as a theoretical tool, demonstrating its capacity to generate realistic, recurring seasonal outbreaks under plausible parameter assumptions. Then the model was calibrated using real-world influenza data from Ontario, Canada, from 2014 to 2019. Smoothing methods, such as a Gaussian kernel, are applied to avoid unrealistic jumps in transmission rates. A systematic optimization using a coarse grid search followed by stochastic refinement calibrates the model to the observed data. The study highlights the potential of modular arithmetic in enhancing the understanding of seasonal infectious diseases.
