Mathematics of Epidemics on Networks

From Exact to Approximate Models

  • István Z. Kiss
  • Joel C. Miller
  • Péter L. Simon

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 46)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 1-26
  3. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 27-66
  4. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 67-115
  5. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 117-164
  6. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 165-205
  7. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 207-253
  8. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 255-272
  9. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 273-301
  10. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 303-326
  11. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 327-365
  12. István Z. Kiss, Joel C. Miller, Péter L. Simon
    Pages 367-379
  13. Back Matter
    Pages 381-413

About this book

Introduction

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 the differential equation models or directly simulate epidemics in 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 biology departments alike. 

Keywords

Dynamic Processes Mathematical Modeling Propagation Models Epidemics Stochastic processes Mean-field models Pairwise models Edge based compartmental model Percolation theory Dynamic/adaptive network Non-Markovian epidemics

Authors and affiliations

  • István Z. Kiss
    • 1
  • Joel C. Miller
    • 2
  • Péter L. Simon
    • 3
  1. 1.Department of MathematicsUniversity of SussexFalmer, BrightonUnited Kingdom
  2. 2.Applied MathematicsInstitute for Disease ModelingBellevueUSA
  3. 3.Institute of MathematicsEötvös Loránd UniversityBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-50806-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-50804-7
  • Online ISBN 978-3-319-50806-1
  • Series Print ISSN 0939-6047
  • Series Online ISSN 2196-9973
  • About this book
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