Compartmental Modeling With Networks

This new advanced text/reference book presents compartmental models or flow models from an applications perspective. Essential topics and methods are introduced in an accessible style with many examples, providing a thorough and comprehensive presentation of compartmental models, model construction and applications.

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.

This timely, authoritative reference covers a breadth of topics in the fields of circuit-switched communications and data networks. It focuses on methodologies for developing network models and techniques for analyzing numerous types and aspects of networks. Bringing together in one complete source a vast amount of information on recent technological advances, Network Modeling, Simulation, and Analysis examines applications of compartmental models to engineering ... network models for the performance analysis of local area computer networks ... closed-form solutions for the evaluation of network performance measures ... adaptive routing and design algorithms for reliable distributed networks ... mixed voice/data networks ... and more. Illustrating concepts with examples from actual case studies, more than 650 display equations, and numerous figures and tables, this exemplary resource is invaluable reading for electrical and electronics, communications, performance, control, industrial, systems, and manufacturing engineers; computer scientists/engineers; operations research scientists; applied mathematicians; and advanced undergraduate and graduate students in these disciplines. Book jacket.

Explores the emerging subject of epidemic dynamics on complex networks, including theories, methods, and real-world applications Throughout history epidemic diseases have presented a serious threat to human life, and in recent years the spread of infectious diseases such as dengue, malaria, HIV, and SARS has captured global attention; and in the modern technological age, the proliferation of virus attacks on the Internet highlights the emergent need for knowledge about modeling, analysis, and control in epidemic dynamics on complex networks. For advancement of techniques, it has become clear that more fundamental knowledge will be needed in mathematical and numerical context about how epidemic dynamical networks can be modelled, analyzed, and controlled. This book explores recent progress in these topics and looks at issues relating to various epidemic systems. Propagation Dynamics on Complex Networks covers most key topics in the field, and will provide a valuable resource for graduate students and researchers interested in network science and dynamical systems, and related interdisciplinary fields. Key Features: Includes a brief history of mathematical epidemiology and epidemic modeling on complex networks. Explores how information, opinion, and rumor spread via the Internet and social networks. Presents plausible models for propagation of SARS and avian influenza outbreaks, providing a reality check for otherwise abstract mathematical modeling. Considers various infectivity functions, including constant, piecewise-linear, saturated, and nonlinear cases. Examines information transmission on complex networks, and investigates the difference between information and epidemic spreading.

This timely overview and synthesis of recent work in both artificial neural networks and neurobiology seeks to examine neurobiological data from a network perspective and to encourage neuroscientists to participate in constructing the next generation of neural networks.

It is always confusing, and perhaps inconvenient at times, using generic terms that will mean something to everyone but different things to different people. "High Performance" is one of those terms. High Performance can be viewed as synonymous to High Speed or Low Latency or a number of other characteristics. The interesting thing is that such ambiguity can sometimes be useful in a world where focus shifts quite easily from one issue to another as times and needs evolve. Many things have changed since the first HPN conference held in Aachen, Germany in 1987. The focus then was mainly on Media Access Control (MAC) protocols that allow users to share the high bandwidth of optical fiber. FDDI (Fiber Distributed Data Interface) was making its debut with its amazing 100 Mbps speed. ATM (Asynchronous Transfer Mode) and SONET (the Synchronous Optical Network) were beginning to capture our imagination. What could users possibly do with such "high performance"? Share it! After realizing that the real problems had gradually shifted away from the network media to the periphery of the network, focus also began to shift. Adapter design, protocol implementation, and communication systems architecture began to attract our interest. Networking -not Networks-became the hot issue.