Unraveling hybrid diffusion structures in epidemics: a bayesian spatiotemporal modeling framework

Infectious disease epidemics in complex urban environments often exhibit hybrid diffusion dynamics that combine localized expansion with sporadic long-distance relocation. Traditional spatial statistical models, such as Conditional Autoregressive (CAR) models, typically rely on fixed, adjacency-based spatial weight matrices, creating risks of structural misspecification when transmission pathways deviate from geographic proximity. To address this limitation, this study develops a Bayesian spatiotemporal modeling framework that treats the spatial weight matrix W as an estimable quantity rather than a fixed input, employing an adaptive CAR prior to infer latent diffusion networks directly from routine surveillance data. This reframing allows the model to distinguish expansion-type from relocation-type connectivity links without requiring pre-specified mobility data. The framework is first evaluated through simulation experiments, demonstrating strong capacity to identify the structural distinction between expansion-type and relocation-type diffusion links (Pearson’s correlation > 0.8). We then apply the model to the 2015 dengue outbreak in Tainan, Taiwan. The inferred diffusion network reveals a distinct hybrid topology: the urban core is sustained by a mixture of contiguous expansion links (30%) and within-cluster relocation links (46%), whereas peripheral districts are predominantly seeded by external relocation links (67%) originating from the core. Community detection further delineates spatial clusters that reflect underlying socio-spatial interactions rather than administrative boundaries. By reframing the adaptive CAR prior as a network inference mechanism, this study provides a flexible and data-driven approach for uncovering complex diffusion pathways and guiding targeted surveillance strategies in settings where detailed mobility data are unavailable.