Initialization and Curing Policies for Polya Contagion Networks

This paper investigates optimization policies for resource distribution in network epidemics using a model that derives from the classical Polya process. The basic mechanics of this model, called the Polya network contagion process, are based on a modified urn sampling scheme that accounts for both temporal and spatial contagion between neighbouring nodes in a network. We present various infection metrics and use them to develop two problems: one which takes place upon initialization and one which occurs continually as the Polya network process develops. We frame these problems as resource allocation problems with fixed budgets, and analyze a suite of potential policies. Due to the complexity of these problems, we introduce effective proxy measures for the average infection rate in each case. We also prove that the two-sided infection-curing game on the so-called expected network exposure admits a Nash equilibrium. In both the curing and initialization scenarios, we introduce heuristic policies that primarily function on the basis of limiting the number of targeted nodes within a particular network setup. Simulations are run for mid-to-large scale networks to compare performance of our heuristics to provably convergent gradient descent algorithms run on the simplified proxy measures.