Spreading phenomena in networks
Spreading phenomena are ubiquitous in our increasingly interconnected world. Understanding how topologically complex interaction patterns affect spreading processes is a goal of huge interest, both theoretically and for applications. In the investigation of these phenomena, simple models for disease transmission play a paradigmatic role. In these lectures, I will give an overview of the most relevant questions in this area and the main results obtained in the last years.
I will start with a very brief introduction to complex networks. I will then focus on the most basic models for the spreading of infectious diseases (SIR and SIS dynamics) on static networks. The interplay between these simple dynamics and the topological properties of the substrate gives rise to nontrivial emergent behavior that requires refined theoretical approaches to be understood. I will then discuss some more specific topics:
- optimal immunization strategies;
- influential spreaders;
- epidemics in temporal, adaptive and multiplex networks;
- interacting epidemics;
- complex contagion (rumors, information spreading, etc...).