# 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
()
or
Richard G. Clegg (richard@richardclegg.org)