Controlling Metastable Infection Patterns in Multilayer Networks via Interlink Design

Recent research on epidemic spreading in networks has uncovered the phenomena of metastable infection patterns, where epidemics can be sustained in localized regions of activity, in contrast to the classical dichotomy between a quick extinction of infections and a network-wide global infection. Our objective in this work is to leverage this localized infection state to achieve controlled spreading in multilayer networks via intelligent design of the interlink structure between the network layers. Following the approach in recent works, the dynamic contact process is approximated by studying the dynamics in local regions around the hubs of the network. This allows us to approximately track the contact process in the near-threshold regime and estimate the mean metastable infection size over the lifetime of the infection. Furthermore, interlinking strategies are devised that can achieve a desired infection size under certain conditions. Theoretically optimal interlink structures can be derived under special cases, whereas greedy strategies are proposed for the general case. We compare the interlinking strategies developed in this work to some popular heuristics and demonstrate their superiority by extensive simulation experiments on both synthetic and real-world networks.