Abstract
We analyze COVID-19 surveillance data from Ontario, Canada, using state-space modelling techniques to address key challenges in understanding disease transmission dynamics. The study applies component linear Gaussian state-space models to capture periodicity, trends, and random fluctuations in case counts. We explore the relationships between COVID-19 cases, hospitalizations, workdays, and wastewater viral loads through dynamic regression models, offering insights into how these factors influence public health outcomes. Our analysis extends to multivariate covariance estimation, utilizing a novel methodology to provide time-varying correlation estimates that account for non-stationary data. Results demonstrate the significance of incorporating environmental covariates, such as wastewater data, in improving model robustness and uncovering the complex interplay between epidemiological factors. This work highlights the limitations of simpler models and emphasizes the advantages of state-space approaches for analyzing dynamic infectious disease data. By illustrating the application of advanced modelling techniques, this study contributes to a deeper understanding of disease transmission and informs public health interventions.