Optimal resource allocation for competing epidemics over arbitrary networks

Abstract

This paper studies an SI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> SI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> S spreading model of two competing behaviors over a bilayer network. In particular, we address the problem of determining resource allocation strategies that ensure the extinction of one behavior while not necessarily ensuring the extinction of the other, and pose a marketing problem in which such a model can be of use. Our discussion begins by extending the SI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> SI <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> S model to node-dependent infection and recovery parameters and generalized graph topologies, contrasting prior work. We then find conditions under which a chosen epidemic becomes extinct. We show that a distribution of resources which realizes this goal always exists for some budget under mild assumptions. We address the case in which the available budget is not sufficient for extinction by establishing analytic means for mitigating the spreading rate of the unwanted behavior. We demonstrate a method for tractably computing solutions to each problem via geometric programming. Our results are validated through simulation.