In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and socio-technical systems. The complex properties of real world networks have a profound impact on the behavior of equilibrium and non-equilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. Here we present a coherent and comprehensive review of the vast research activity concerning epidemic processes, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, epidemiologists, computer and social scientists share a common interest in studying epidemic spreading and rely on very similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while we focus on the main results and the paradigmatic models in infectious disease modeling, we also present the major results concerning generalized social contagion processes. Finally we outline the research activity at the forefront in the study of epidemic spreading in co-evolving and time-varying networks.
Epidemic processes in complex networks
Romualdo Pastor-Satorras, Claudio Castellano, Piet Van Mieghem, Alessandro Vespignani