An interaction Neyman–Scott point process model for coronavirus disease-19

With rapid transmission, the coronavirus disease 2019 (COVID-19) has led to over three million deaths worldwide, posing significant societal challenges. Understanding the spatial patterns of patient visits and detecting local cluster centers are crucial to controlling disease outbreaks. We analyze COVID-19 contact tracing data collected from Seoul, which provide a unique opportunity to understand the mechanism of patient visit occurrence. Analyzing contact tracing data is challenging because patient visits show strong clustering patterns, while cluster centers may have complex interaction behavior. Cluster centers attract each other at mid-range distances because other cluster centers are likely to appear in nearby regions. At the same time, they repel each other at too small distances to avoid merging. To account for such behaviors, we develop a novel interaction Neyman–Scott process that regards the observed patient visit events as offsprings generated from a parent cluster center. Inference for such models is challenging since the likelihood involves intractable normalizing functions. To address this issue, we embed an auxiliary variable algorithm into our Markov chain Monte Carlo. We fit our model to several simulated and real data examples under different outbreak scenarios and show that our method can describe the spatial patterns of patient visits well. We also provide useful visualizations that can inform public health interventions for infectious diseases, such as social distancing.