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Cover: 9783319508047 | Mathematics of Epidemics on Networks | Istvan Z. Kiss (u. a.) | Buch
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Mathematics of Epidemics on Networks
From Exact to Approximate Models
Buch von Istvan Z. Kiss (u. a.)
Sprache: Englisch

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Beschreibung
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 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.
Über den Autor
Dr. I.Z. Kiss: Dr. Kiss is a Reader in the Department of Mathematics at the University of Sussex with his research at the interface of network science, stochastic processes and dynamical systems. His work focuses on the modeling and analysis of stochastic epidemic processes on static and dynamic networks. His current interests include the identification of rigorous links between approximate models and their rigorous mathematical counterparts and formulating new models for more complex spreading processes or structured networks.
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.
Zusammenfassung

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: [...]

Inhaltsverzeichnis
Preface.- ¿Introduction to Networks and Diseases.- Exact Propagation Models: Top Down.- Exact Propagation Models: Bottom-Up.- Mean-Field Approximations for Heterogeneous Networks.- Percolation-Based Approaches for Disease Modelling.- Hierarchies of SIR Models.- Dynamic and Adaptive Networks.- Non-Markovian Epidemics.- PDE Limits for Large Networks.- Disease Spread in Networks with Large-scale structure.- Appendix: Stochastic Simulation.- Index.
Details
Erscheinungsjahr: 2017
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Interdisciplinary Applied Mathematics
Inhalt: xviii
413 S.
41 s/w Illustr.
89 farbige Illustr.
413 p. 130 illus.
89 illus. in color.
ISBN-13: 9783319508047
ISBN-10: 3319508040
Sprache: Englisch
Einband: Gebunden
Autor: Kiss, Istvan Z.
Miller, Joel C.
Simon, Péter L.
Hersteller: Springer-Verlag GmbH
Springer International Publishing AG
Abbildungen: 42 schwarz-weiße und 79 farbige Abbildungen, Bibliographie
Maße: 241 x 160 x 29 mm
Von/Mit: Istvan Z. Kiss (u. a.)
Erscheinungsdatum: 22.05.2017
Gewicht: 0,811 kg
Artikel-ID: 109144991
Über den Autor
Dr. I.Z. Kiss: Dr. Kiss is a Reader in the Department of Mathematics at the University of Sussex with his research at the interface of network science, stochastic processes and dynamical systems. His work focuses on the modeling and analysis of stochastic epidemic processes on static and dynamic networks. His current interests include the identification of rigorous links between approximate models and their rigorous mathematical counterparts and formulating new models for more complex spreading processes or structured networks.
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.
Zusammenfassung

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: [...]

Inhaltsverzeichnis
Preface.- ¿Introduction to Networks and Diseases.- Exact Propagation Models: Top Down.- Exact Propagation Models: Bottom-Up.- Mean-Field Approximations for Heterogeneous Networks.- Percolation-Based Approaches for Disease Modelling.- Hierarchies of SIR Models.- Dynamic and Adaptive Networks.- Non-Markovian Epidemics.- PDE Limits for Large Networks.- Disease Spread in Networks with Large-scale structure.- Appendix: Stochastic Simulation.- Index.
Details
Erscheinungsjahr: 2017
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Interdisciplinary Applied Mathematics
Inhalt: xviii
413 S.
41 s/w Illustr.
89 farbige Illustr.
413 p. 130 illus.
89 illus. in color.
ISBN-13: 9783319508047
ISBN-10: 3319508040
Sprache: Englisch
Einband: Gebunden
Autor: Kiss, Istvan Z.
Miller, Joel C.
Simon, Péter L.
Hersteller: Springer-Verlag GmbH
Springer International Publishing AG
Abbildungen: 42 schwarz-weiße und 79 farbige Abbildungen, Bibliographie
Maße: 241 x 160 x 29 mm
Von/Mit: Istvan Z. Kiss (u. a.)
Erscheinungsdatum: 22.05.2017
Gewicht: 0,811 kg
Artikel-ID: 109144991
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