Overview
- Details the current state-of-the-art in modeling epidemics on networks
- Offers direct comparison of the main network epidemic models and works out their hierarchy
- Identifies opportunities for further rigorous mathematical exploration
- Features practical simulation algorithms written in pseudocode with implemented code available online
- Includes supplementary material: sn.pub/extras
Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 46)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
- 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.
Reviews
“This is one of the first books to appear on modeling epidemics on networks. … This is a comprehensive and well-written text aimed at students with a serious interest in mathematical epidemiology. It is most appropriate for strong advanced undergraduates or graduate students with some background in differential equations, dynamical systems, probability and stochastic processes.” (William J. Satzer, MAA Reviews, September, 2017)
Authors and Affiliations
About the authors
Dr. J.C. Miller: Dr. Miller is a Senior Research Scientist at the Institute for Disease Modeling in Seattle. He is also a Senior Lecturer at Monash University in Melbourne with a joint appointment in Mathematics and Biology. His research interests include dynamics of infectious diseases, stochastic processes on networks, and fluid flow in porous media. The majority of his work is at the intersection of infectious disease dynamics and stochastic processes on networks.
Prof. P.L. Simon: Prof. Simon is a Professor at the Institute of Mathematics, Eötvös Loránd University, Budapest. He is a member of the Numerical Analysis and Large Networks research group and the Head of Department of Applied Analysis and Computational Mathematics. His research interests include dynamical systems, partial differential equations and their applications in chemistry and biology. In particular, his work focuses on the modeling and analysis of network processes using differential equations.
Bibliographic Information
Book Title: Mathematics of Epidemics on Networks
Book Subtitle: From Exact to Approximate Models
Authors: István Z. Kiss, Joel C. Miller, Péter L. Simon
Series Title: Interdisciplinary Applied Mathematics
DOI: https://doi.org/10.1007/978-3-319-50806-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-50804-7Published: 22 May 2017
Softcover ISBN: 978-3-319-84494-7Published: 28 July 2018
eBook ISBN: 978-3-319-50806-1Published: 08 June 2017
Series ISSN: 0939-6047
Series E-ISSN: 2196-9973
Edition Number: 1
Number of Pages: XVIII, 413
Number of Illustrations: 41 b/w illustrations, 89 illustrations in colour
Topics: Mathematical and Computational Biology, Dynamical Systems and Ergodic Theory, Applications of Graph Theory and Complex Networks, Epidemiology, Probability Theory and Stochastic Processes