State-space modelling for infectious disease surveillance data: Stochastic simulation techniques and structural change detection

We present an exploration of advanced stochastic simulation techniques for state-space models, with a specific focus on their applications in infectious disease modelling. Utilizing COVID-19 surveillance data from the province of Ontario, Canada, we employ Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods to detect structural changes and pre-dict future trends in case counts. Our approach begins with the application of a Kalman smoothing technique, integrated with MCMC for state sampling within local level and seasonal models, alongside Bayesian inference for non-linear dynamic regression models. We then assess the effectiveness of various priors, including normal, Student's t, Laplace, and horseshoe distributions, in capturing abrupt changes within the data using a Rao-Blackwellized par-ticle filter. Our findings highlight the superior performance of the horseshoe prior in identifying change points and adapting to complex data structures, offering valuable insights for real-time monitoring and forecasting in public health. This study emphasizes the efficacy of state-space models, particu-larly when enhanced with sophisticated prior distributions, in providing a nuanced understanding of infectious disease transmission.