Effective Network Quarantine with Minimal Restrictions on Communication Activities

This paper studies a network structure design problem constrained by the epidemic outbreaks. In our model, geographic locations (nodes) and their connections (edges) are modeled as a ring graph. The movement of a person is represented as a flow from one location to another. A person can be infected at a location (node), depending on the number of infected flows (persons) going through that location. In our paper, diseases are not limited to real human diseases; they can also refer to the general epidemic information propagations. Given desired interaction traffic from a node to other nodes in terms of flows, and a greedy shortest path routing scheme that is analogous to the greedy coin change, we focus on the structure design (representing quarantine rules) that determines the number and distribution of chords on the virtual ring network for remote connections. Our objective is to minimize the average number of routing hops, while the epidemic outbreaks are controlled under given infection and recovery rates. We provide a systematic isomorphic structure design on nine different cases, based on three traffic distribution and three infection rate models. Two hypercube-based structures are proposed. We also provide a greedy solution for constructing polymorphic structures. Our study reveals some intriguing theoretical results, validated through experiments, on tradeoffs between local and global infections. Our work casts new light on the effective network quarantine that places minimal restrictions on connections, i.e., maximal preservation of normal communication activities, while controlling epidemic outbreaks.