Summary

Adaptive networks, which combine topological evolution of the network with dynamics on the network, are ubiquitous across disciplines. Examples include technical distribu-tion networks such as road networks and the internet, natural and biological networks, and social science net-works. These networks often interact with or depend upon other networks, resulting in multilayer adaptive networks. We study susceptible-infected-susceptible (SIS) epidemic dynamics on such networks revealing a new stable state which only emerges in the case of weakly coupled net-works [5]. In this state, the disease is endemic in one network but neither becomes endemic nor dies out in the other. Instead, it persists only at the interconnected nodes and does not break out into the wider network. Additional details We consider two networks A and B with the same number of nodes NA = NB = N, where a randomly chosen fraction of nodes pcoup from each network are connected through inter-network connections to nodes in the other network [2, 1], see Fig. 1. We extend Gross et al.’s model of SIS epidemic dynam-ics on adaptive networks [4] from a single to multilayer networks. Nodes in both networks can be in either one of two states – susceptible or infected – where susceptible nodes can get infected from their intra- and inter-network neighbors and infected nodes can recover and become susceptible again. In addition, each network is indepen-dently adaptive in the sense that susceptible nodes can rewire their intra-network edges from infected neighbors to randomly selected susceptible ones. However, the inter-links connecting between networks are permanent (nonadaptive). This limits an individual network’s ability to adapt in the face of challenges, since it can change its own topology but not its dependence on other networks. In geographically distant social net-works, for example, long-distance links are often family links which are not subject to rewiring compared to short-distance friend and acquaintance links