Title: A Polya Contagion Model for Networks,
Abstract: A network epidemics model based on the classical Polya urn scheme is
investigated. Temporal contagion processes are generated on the network nodes
using a modified Polya sampling scheme that accounts for spatial infection
among neighbouring nodes. The stochastic properties and the asymptotic
behaviour of the resulting network contagion process are analyzed. Unlike the
classical Polya process, the network process is noted to be non-stationary in
general, although it is shown to be time-invariant in its first and some of its
second-order statistics and to satisfy martingale convergence properties under
certain conditions. Three classical Polya processes, one computational and two
analytical, are proposed to statistically approximate the contagion process of
each node, showing a good fit for a range of system parameters. Finally,
empirical results compare and contrast our model with the well-known discrete
time SIS model.