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© 2017

Mathematics of Epidemics on Networks

From Exact to Approximate Models

Textbook

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

  1. 1.Department of MathematicsUniversity of SussexFalmer, BrightonUnited Kingdom
  2. 2.Applied MathematicsInstitute for Disease ModelingBellevueUSA
  3. 3.Institute of MathematicsEötvös Loránd UniversityBudapestHungary

About the authors

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.

Bibliographic information

Reviews

“The book adds to the knowledge of epidemic modeling on networks by providing a number of rigorous mathematical arguments and confirming the validity and optimal range of applicability of the epidemic models. It serves as a good reference guide for researchers and a comprehensive textbook for graduate students.” (Yilun Shang, Mathematical Reviews, November, 2017)

“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)