Spatial community structure and epidemics

Networks are a useful quantitative representation for complex systems of interacting entities arising in fields such as biological, physical and social sciences. A network representation provides a degree of simplification while capturing key connectivity patterns. This thesis focuses on two main themes: the study of community structure, an important mesoscopic feature of many networks, and its application to study spatiotemporal spread of infectious diseases. Community detection seeks to partition a network into dense sets of nodes that are connected sparsely to other dense sets. The notion of denseness is often relative to some "null model" that describes baseline connectivity that can be construed to occur randomly. In the first part of the thesis, we discuss the incorporation of spatial information into null models for community detection. We develop a spatial null model based on the radiation model of mobility. We test different spatial null models using static and temporal (multilayer) spatial benchmarks with planted partitions that represent interactions between human populations. Our results indicate that it is important to incorporate spatial information into null models for community detection, but it is best to incorporate only relevant information into null models, as extraneous information can lower performance. In the second part of the thesis, we present the results of community detection with different null models on disease-correlation networks generated form real and synthetic time series of disease occurrence. We use data sets for endemic diseases (established in a region, with occasional epidemic outbreaks) and emerging diseases (newly-discovered or introduced into a region for the first time). We study the spatial and temporal organization of partitions. Finally, we apply community detection with different null models to synthetic time series generated from an agent-based model (ABM) simulating the spread of endemic and emerging diseases between spatially-embedded cities with a planted, transport-based community structure. We compare the findings on real and synthetic data sets, and we searched for model parameter regimes in which we are able to detect planted partitions or other interesting communities. For emerging diseases, we find spatial communities that are associated with the first times the infection reached a node in both ABM and disease data. For endemic diseases, we are unable to find planted or spatial communities in the ABM data, but we detect spatial communities for two of the three disease data sets. For these diseases, we also detect temporal communities corresponding to some of the important time points in disease history. We hope that these results show that community structure of disease correlation networks appears to be more complicated than simple spatial patterns and is a fascinating topic to study.