E Valdano, M Re Fiorentin, C Poletto, V Colizza
The complex interplay between spreading dynamics on a network and underlying time-evolving topologies challenges our understanding of these phenomena. Specifically, contacts’ evolution impacts the conditions leading to the wide-spreading regime. In this work we introduce a novel theoretical framework for analytically predicting the epidemic threshold for any temporal network, extending the infection propagator approach (Valdano et al. Phys Rev X 2015) to continuous time evolving patterns. This allows us to go beyond previously used approximations, such as discretization, known to possibly bias results. We also provide an explicit solution applicable to contexts of interest and provide a mathematical formulation to reinterpret the widely used concept of annealing. Our findings offer the first systematic connection between the discrete and continuous formulations of spreading phenomena on arbitrary evolving networks.