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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 textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.
Provides the mathematical, stochastic and graph theoretic methods to analyse the performance and robustness of complex networks and systems.
This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate students taking courses in performance analysis.
A comprehensive introduction to the theory and applications of complex network science, complete with real-world data sets and software tools.
This book gathers the proceedings of the 13th International Conference on Management Science and Engineering Management (ICMSEM 2019), which was held at Brock University, Ontario, Canada on August 5–8, 2019. Exploring the latest ideas and pioneering research achievements in management science and engineering management, the respective contributions highlight both theoretical and practical studies on management science and computing methodologies, and present advanced management concepts and computing technologies for decision-making problems involving large, uncertain and unstructured data. Accordingly, the proceedings offer researchers and practitioners in related fields an essential update, as well as a source of new research directions.
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.
The emergence of severe acute respiratory syndrome (SARS) in late 2002 and 2003 challenged the global public health community to confront a novel epidemic that spread rapidly from its origins in southern China until it had reached more than 25 other countries within a matter of months. In addition to the number of patients infected with the SARS virus, the disease had profound economic and political repercussions in many of the affected regions. Recent reports of isolated new SARS cases and a fear that the disease could reemerge and spread have put public health officials on high alert for any indications of possible new outbreaks. This report examines the response to SARS by public health systems in individual countries, the biology of the SARS coronavirus and related coronaviruses in animals, the economic and political fallout of the SARS epidemic, quarantine law and other public health measures that apply to combating infectious diseases, and the role of international organizations and scientific cooperation in halting the spread of SARS. The report provides an illuminating survey of findings from the epidemic, along with an assessment of what might be needed in order to contain any future outbreaks of SARS or other emerging infections.
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the VI International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2017), which took place in Lyon on November 29 – December 1, 2017. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and ecological networks and technological networks.