Measuring spatial inhomogeneity at different spatial scales using hybrids of Gibbs point process models

Abstract

Infectious diseases give rise to complex spatial patterns exhibiting aggregation at different scales. Baddeley (J Stat Softw 55:1–43, 2013) proposed a technique for constructing new Gibbs models for spatial point patterns, combining existing models available in the literature. We use their proposal to model the spatial point pattern of varicella, a highly contagious airborne disease, in Valencia, Spain. We employed descriptive analysis to get a glimpse of the basic properties of the point pattern. Covariate information such as the density of population (children under 14 years old) living in the study region, the distance to the nearest school, and the composition of families (expressed as the average number of persons per family) is used to describe the intensity of the process. We used SatScan to identify main clusters of schools, and to feed the model with this further information. Our analysis shows the relation between varicella cases and school locations, and highlights aggregation in the data at different spatial scales.