Epidemic Spreading in Temporal and Adaptive Networks with Static Backbone

Activity-driven networks (ADNs) are a powerful paradigm to study epidemic spreading in temporal networks, where the dynamics of the disease and the evolution of the links share a common time-scale. One of the key assumptions of ADNs is the lack of preferential connections among individuals. This assumption hinders the application of ADNs to several realistic scenarios where some contacts persist in time, rather than intermittently activate. Here, we examine an improved modeling framework that superimposes an ADN to a static backbone network, toward the integration of persistent contacts with time-varying connections. To demonstrate the interplay between the ADN and the static backbone, we investigate the effect of behavioral changes on the disease dynamics. In this framework, each individual may adapt his/her activity as a function of the health status, thereby adjusting the relative weight of time-varying versus static links. To illustrate the approach, we consider two classes of backbone networks, Erdős-Rényi and random regular, and two disease models, SIS and SIR. A general mean-field theory is established for predicting the epidemic threshold, and numerical simulations are conducted to shed light on the role of network parameters on the epidemic spreading and estimate the epidemic size.