Epidemiologically optimal static networks from temporal network data

Network epidemiology's most important assumption is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.