Control of epidemics on complex networks: Effectiveness of delayed isolation

We study isolation as a means to control epidemic outbreaks in complex networks, focusing on the consequences of delays in isolating infected nodes. Our analysis uncovers a tipping point: if infected nodes are isolated before a critical day d(c), the disease is effectively controlled, whereas for longer delays the number of infected nodes climbs steeply. We show that d(c) can be estimated explicitly in terms of network properties and disease parameters, connecting lowered values of d(c) explicitly to heterogeneity in degree distribution. Our results reveal also that initial delays in the implementation of isolation protocols can have catastrophic consequences in heterogeneous networks. As our study is carried out in a general framework, it has the potential to offer insight and suggest proactive strategies for containing outbreaks of a range of serious infectious diseases.