Similarity- and neighbourhood-based dynamic models for infection data: Uncovering the complexities of the COVID-19 infection risks.

Understanding spatial and temporal risk dependencies and correlation is crucial when studying infectious diseases which spread out in consecutive waves. By analysing weekly COVID-19 case data collected from the disease's first reported case on March 3, 2020, to April 22, 2021, in 278 municipalities in Mainland Portugal, we demonstrate that the complexity of infection risks varies based on the outbreak's severity, suggesting that a single model definition is insufficient to explain the multifaceted underlying phenomena. This study employs a dynamic, conditionally specified Gaussian Markov random field model with a novel approach to characterise COVID-19 infection risk dependencies through the similarity of areal-level covariates within a Bayesian hierarchical model framework that accounts for each identifiable wave. The results indicate that the neighbourhood-based conditional autoregressive model, which is static and based on an adjacency-based neighbourhood matrix, do not necessarily captures the disease's complex spatial-temporal nature. Furthermore, the best-fitting dynamic model may not necessarily be the best predicting model in certain situations, which can lead to inadequate resource allocation in epidemic situations. Accurate forecasting can help inform decisions regarding difficult-to-measure impacts, potentially saving lives. Implementing the proposed novel approach would have produced information that would have been overwhelmingly critical to the respective authorities in protecting those in more unfavourable economic or other conditions.