  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 sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium 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. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.
