A Polya urn-based model for epidemics on networks

A network epidemics model based on the classical Polya urn scheme is investigated. Temporal contagion processes are generated on the network nodes via a modified Polya sampling scheme that accounts for spatial infection among neighboring nodes. The stochastic properties and the asymptotic behavior 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 for certain network structures. Finally, two classical Polya processes, one computational and one analytical, are proposed to statistically approximate the contagion process of each node, showing a good fit for a range of system parameters.