Invited review: Epidemics on social networks

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes. They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases. In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed. These new models incorporated concepts from graph theory to describe and model the underlying social structure. Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the most relevant results in the field.