Epidemics and Rumours in Complex Networks (London Mathematical Society Lecture Note Series, Series Number 369)

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.

Information propagates through large, dynamic communication systems such as peer-to-peer networks, online social systems and mobile ad hoc networks much like viral epidemics. Analysis of stochastic epidemic processes thus provides insights in the operations of modern communication networks and guidance for their design.

This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical results in the field. It introduces classical models of epidemics, including branching processes and more advanced models of random graphs. The main mathematical tools consist of coupling methods, Poisson approximation techniques and large deviations inequalities. The key results covered include phase transitions arising in random graphs and epidemics on general networks, analysis of small-world phenomena and emergence of power laws. Directions for further reading are provided in each chapter. An ideal support for graduate courses in applied mathematics or computer science, this book will also be useful to researchers in statistical physics, biology and social sciences as a modern introduction to modelling of epidemics on networks.

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. --from publisher description