Spatially Correlated Analysis of Infectious Disease Outcomes Based on Bayesian Functional Hierarchical Models

Prevalent infectious diseases, such as COVID-19, have triggered widespread social panic and placed immense strain on global healthcare systems. Understanding the complex spatio-temporal dynamics of these diseases and accurately forecasting their progression are essential for effective public health interventions. Existing forecasting paradigms struggle to simultaneously resolve three fundamental challenges: (1) temporal misalignment of epidemic curves across regions, (2) spatial dependency structures in transmission dynamics, and (3) persistent overdispersion in count data. This paper develops a novel Bayesian hierarchical model tailored to spatially correlated functional count data to analyze and predict the trajectories of case counts across different regions. Our key innovations address critical gaps in pandemic analytics. By implementing a curve preprocessing step, the proposed model aligns the epidemic curves, facilitating better comparison across regions with staggered outbreak timings. The Negative-Binomial distribution is employed to accommodate data overdispersion, while the temporal dynamics are captured using nonparametric basis functions, allowing for flexible and accurate modeling of disease trajectories. Spatial correlation among regions is modeled through a Leroux conditional autoregressive prior, which adapts to varying degrees of spatial dependency. An efficient Gibbs sampler is developed to derive posterior inferences and multi-step ahead forecasting distributions. Simulation studies demonstrate substantial improvements of the proposed model in estimation accuracy and prediction precision compared to several alternative approaches. Applied to COVID-19 case data across U.S. states, the model provides critical insights into the time-varying effects of key covariates. It also enables the early prediction of case surges in states with delayed outbreak trajectories, offering valuable tools for resource allocation and strategic planning.