Initialization and Curing Policies for Polya Contagion Networks

TL;DR

This paper explores resource allocation strategies for controlling network epidemics modeled by a Polya process, proposing heuristics and analyzing equilibrium conditions through simulations and proxy measures.

Contribution

It introduces new initialization and curing policies for Polya network contagion models, along with heuristic algorithms and equilibrium analysis.

Findings

Heuristic policies effectively limit infection spread.

Nash equilibrium exists for the infection-curing game.

Simulations show competitive performance of heuristics against gradient methods.

Abstract

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.