Measuring cluster interactions through in-between areas in epidemic spatiotemporal dynamics

Understanding interactions between spatiotemporal clusters is essential for effective epidemic control. Cluster interaction occurs when a location belongs to multiple clusters at different times, indicating spatial but not temporal overlap. However, such overlap alone does not fully explain how clusters are linked or how transmission pathways form across them. Analytical frameworks to examine these dynamics remain limited. This study introduces the concept of “in-between areas”, transitional zones, that connect clusters through shared transmission routes. We propose a novel framework that integrates causal analysis with network community detection to identify clusters, detect in-between areas, and quantify their interactions. Applied to the 2014 dengue outbreak in Kaohsiung, Taiwan, the results reveal that in-between areas shift from administrative boundaries to interior districts as the epidemic progresses, indicating evolving cluster interactions. These areas link locations across different clusters, exposing the complex structure of spatial diffusion. Quantitative findings show that dominant clusters often absorb smaller ones, with the latter frequently initiating transmission into new regions. The proposed framework identifies both the timing and spatial configuration of cluster interactions, offering new insights into epidemic spread. This approach advances spatial epidemiology by supporting the design of targeted, mobility-aware public health interventions.