MoN18: Eighteenth Mathematics of Networks meeting

Francesco di Lauro (Sussex) Network inference from population-level observation of epidemics

The network paradigm is widely accepted as the gold standard in modelling complex systems such as epidemics spreading on networks or neuronal activity in the brain; however, in most cases, the exact nature of the network on which such dynamics unfold is unknown. This has motivated a significant amount of work on network infer- ence. Whilst a large body of work is concerned with inferring the network structure provided detailed node-level temporal data, in this work we attempt to tackle the more challenging scenario of inferring the family of the underlying network when only population-level incidence data are available. This is done by first approximating the SIS epidemic on a network by a Birth-Death process whose rates encode the structure of the network and disease dynamics. Using systematic and extensive simulations, we propose a parsimonious (three-parameter) model of these rates and show that different well-known network families map onto distinct regions of the parameter space of this model. Using kernel-density estimation, we construct priors for these families of networks. Then, given population-level temporal epidemic data, we employ Bayesian inference to derive a posterior distribution over these model parameters and identify the most likely network family. We believe that our framework generalises readily to many network families and spreading processes and that it could provide a new benchmark in network inference from population-level data.

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Contact: Keith Briggs (mailto:keith.briggs_at_bt_dot_com) or Richard G. Clegg (