Epidemics and Rumours in Complex Networks

Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with network topology allows us to predict ultimate course, understand phase transitions and develop strategies to control and optimise dissemination. This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling methods, Poisson approximation (the Stein-Chen method), concentration inequalities (Chernoff bounds and Azuma-Hoeffding inequality) and branching processes. The authors examine the small-world phenomenon, preferential attachment, as well as classical epidemics. Each chapter ends with pointers to the wider literature. An ideal accompaniment for graduate courses, this book is also for researchers (statistical physicists, biologists, social scientists) who need an efficient guide to modern approaches to epidemic modelling on networks. 'this is a nice introduction, at the level of a graduate course, to the propagation of biological epidemics and the spread of rumours in networks, aimed at students in computer science and applied probability.' Zentralblatt MATHIntroduction; Part I. Shapeless Networks: 1. Galton-Watson branching processes; 2. Reed-Frost epidemics and Erdos-Renyi random graphs; 3. Connectivity and Poisson approximation; 4. Diameter of Erdos-Renyi graphs; 5. From microscopic to macroscopic dynamics; Part II. Structured Networks: 6. The small-world phenomenon; 7. Power laws via preferential attachment; 8. Epidemics on general graphs; 9. Viral marketing and optimised epidemics; References; Index.