Optimal resource allocation for competitive spreading processes on bilayer networks

TL;DR

This paper develops a resource allocation strategy to control competing spreading processes on bilayer networks, ensuring the extinction of a targeted process efficiently using mean-field approximations and optimization techniques.

Contribution

It extends the SI1SI2S model to include edge-dependent infection and node-dependent recovery, and formulates an optimal resource allocation problem for epidemic extinction.

Findings

Mean-field approximation effectively guides resource allocation for epidemic control.

Optimal strategies minimize expenditure to achieve rapid extinction.

Mean-field methods are less accurate in some stochastic scenarios.

Abstract

This paper studies the SI1SI2S spreading model of two competing behaviors over a bilayer network. We address the problem of determining resource allocation strategies which design a spreading network so as to ensure the extinction of a selected process. Our discussion begins by extending the SI1SI2S model to edge-dependent infection and node-dependent recovery parameters with generalized graph topologies, which builds upon prior work that studies the homogeneous case. We then find conditions under which the mean-field approximation of a chosen epidemic process stabilizes to extinction exponentially quickly. Leveraging this result, we formulate and solve an optimal resource allocation problem in which we minimize the expenditure necessary to force a chosen epidemic process to become extinct as quickly as possible. In the case that the budget is not sufficient to ensure extinction of the desired process, we instead minimize a useful heuristic. We explore the efficacy of our methods by comparing simulations of the stochastic process to the mean-field model, and find that the mean-field methods developed work well for the optimal cost networks designed, but suffer from inaccuracy in other situations.