Curing Epidemics on Networks using a Polya Contagion Model

TL;DR

This paper models epidemic spreading on networks using a Polya urn variation, formulates an optimal curing resource allocation problem, and proposes algorithms and heuristics to effectively minimize infection levels.

Contribution

It introduces a novel network contagion model based on Polya urns, formulates an optimal control problem, and develops algorithms for resource allocation to curb epidemics.

Findings

Gradient descent algorithm effectively allocates curing resources.

Heuristic methods perform nearly as well as optimal strategies.

Simulations on large networks validate the proposed approaches.

Abstract

We study the curing of epidemics of a network contagion, which is modelled using a variation of the classical Polya urn process that takes into account spatial infection among neighbouring nodes. We introduce several quantities for measuring the overall infection in the network and use them to formulate an optimal control problem for minimizing the average infection rate using limited curing resources. We prove the feasibility of this problem under high curing budgets by deriving conservative lower bounds on the amount of curing per node that turns our measures of network infection into supermartingales. We also provide a provably convergent gradient descent algorithm to find the allocation of curing under limited budgets. Motivated by the fact that this strategy is computationally expensive, we design a suit of heuristic methods that are locally implementable and nearly as effective. Extensive simulations run on largescale networks demonstrate the effectiveness of our proposed strategies.