Epidemics and Rumours in Complex Networks (Paperback)

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.

透過點對點系統、線上社交系統、無線移動自組網路和其他現代結構的資訊傳播，可以被建模為在聯絡網路上的傳染病。了解傳染病過程如何與網路拓撲互動，讓我們能夠預測最終的進程，了解階段轉變並制定控制和優化傳播的策略。本書是針對應用數學家和計算機科學家的簡明介紹，介紹基本模型、分析工具以及數學和算法結果。介紹的數學工具包括耦合方法、泊松近似（Stein-Chen方法）、集中不等式（Chernoff界限和Azuma-Hoeffding不等式）和分支過程。作者們探討了小世界現象、優先連結以及經典傳染病。每章結束時都會提供廣泛文獻的指引。這本書是研究生課程的理想伴侶，也適用於需要現代傳染病建模方法的研究人員（統計物理學家、生物學家、社會科學家）。