Impact of inter-layer hopping on epidemic spreading in a multilayer network

Hopping of individuals among distinct layers can induce inter-layer coupling and consequently affect the spreading process in each layer of real world multilayer networks. We articulate a two-layer network model where a fraction of nodes are inter-layer travelers that can hop between layers. We develop a theoretical framework based on the quenched mean-field approximation to accurately predict the epidemic thresholds and final states in both layers. Extensive numerical simulations on synthetic and empirical networks demonstrate that, in the general setting where the structures of the two network layers are asymmetric, intense hopping can lead to simultaneous epidemic outbreak in both layers. In general, the impacts of hopping on the spreading dynamics in the two layers can be quite distinct. As the inter-layer coupling strength is increased, the epidemic threshold of the denser layer increases monotonically, while for the sparser layer, a surprising non-monotonic behavior of the threshold with a minimize value arises. Another finding is that, as a result of hopping, recurrent outbreaks can occur in the sparser layer, providing a plausible explanation for the phenomenon of multiple outbreaks observed from real health data.