Local Reproduction Numbers for Analysis and Optimal Mitigation of Epidemic Processes

Abstract

In this paper, we propose a unifying framework to analyze layered networked epidemic processes where the population, represented either as a networked SIS or SIR model, is coupled with an infrastructure network. We propose novel local metrics that enable the analysis of the epidemic spreading locally (node-level) and the prediction of the network-wide spreading under some sufficient conditions. Inspired by the bilayer nature of our model, we partition the layered network between intra- and inter-layer interactions. We identify conditions at the layer level which allow the characterization of the network-level basic reproduction number in terms of the physical structure of the layered network. Then, we leverage the local metrics to propose an optimization framework for epidemic mitigation based on a fundamental notion: the network-wide spreading can be quantified by the aggregation of the local (node-level) epidemic burden. We provide guarantees that the local metric-based optimization can be solved as a geometric program. We illustrate our theoretical results via numerical examples and evaluate the performance of the local metrics and the optimization framework they enable versus other existing epidemic mitigation approaches based on network-level metrics.