Epidemic Threshold in Temporal Multiplex Networks With Individual Layer Preference

Many efforts have been devoted to understanding how human behaviors induced by the awareness of disease influence the epidemic dynamics in multiplex networks. The awareness and virus spreading is mostly studied with the unaware-aware-unaware-susceptible-infected-susceptible (UAU-SIS) model over a given and fixed (static) network. However, the role of the spatial-temporal properties of multiplex networks to the epidemic spreading is not fully understood. In this work, a temporal multiplex network consists of a static information spreading network and a temporal physical contact network with a layer-preference walk. Defining the tendency of aware nodes moving to a specified layer as the layer preference, we focus on two scenarios: (i) the layer preference is constant, (ii) the layer preference is a function of the degree of nodes in the information layer. We deduce the epidemic threshold of such a temporal multiplex network, and validate it through numerical simulations. Moreover, we find that the epidemic threshold decreases with the decrease of the effective information spreading rate and the increase of the layer preference. Furthermore, we find that when the node with a higher degree displays a higher layer preference, the spreading process on the network is remarkably promoted. The findings shed a new light on the control of the epidemic spreading process.