Suppressing Epidemics in Networks Using Priority Planning

In this paper, we analyze a large class of dynamic resource allocation (DRA) strategies, named priority planning, that aim to suppress SIS epidemics taking place in a network. This is performed by distributing treatments of limited efficiency to its infected nodes, according to a priority-order precomputed offline. Under this perspective, an efficient DRA strategy for a given network can be designed by learning a proper linear arrangement of its nodes. In our theoretical analysis, we derive upper and lower bounds for the extinction time of the diffusion process that reveal the role of the maxcut of the considered linear arrangement. Accordingly, we highlight that the cutwidth, which is the minimum maxcut of all possible linear arrangements for a network, is a fundamental network property that determines the resource budget required to suppress the epidemic under priority planning. Finally, by making direct use of our theoretical results, we propose a novel and efficient DRA strategy, called maxcut minimization (MCM), which outperforms other competing strategies in our simulations, while offering desirable robustness under various noise profiles.