Mathematics of Epidemics on Networks : From Exact to Approximate Models

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 book’s content lies at the interface of epidemiology, graph theory, stochastic processes and dynamical systems. This second edition has been substantially expanded from 11 to 15 chapters, adding comprehensive coverage of stochastic models, statistical inference, simple and complex contagions, and higher-order network structures. New material reflects recent theoretical advances, while maintaining the unified mathematical framework that made the first edition so valuable. 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, including stochastic models, 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;
• Introducing likelihood-based inference frameworks and Bayesian tools for parameter estimation from real epidemic data;
• Extending classical network epidemic models to higher-order structures and complex contagion processes;
• 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.

I.Z. Kiss: Prof. Kiss is a Professor of Network Science at the Network Science Institute within Northeastern University London with his research at the interface of epidemiology, network science, stochastic processes and dynamical systems. His work focuses on modeling and analysis of stochastic processes on static, dynamic and higher-order networks. His research combines mathematical depth with practical impact, advancing both fundamental understanding and applied solutions across domains from public health to technology.

J.C. Miller: A/Prof. Miller is an Associate Professor in the Department of Mathematical and Physical Sciences and a member of the Australian Centre for Artificial Intelligence in Medical Innovation at La Trobe University in Melbourne.  Previously he was a Senior Research Scientist at the Institute for Disease Modeling in Seattle.  His research interests include dynamics of infectious diseases, stochastic processes on networks, and algorithm development for stochastic simulations. 

G.A. Rempala.  Prof. Rempala is Professor of Biostatistics and Mathematics at The Ohio State University, USA. His research lies at the interface of applied probability, stochastic processes, and mathematical biology. He is particularly interested in modelling and analysis of complex dynamical systems arising in epidemiology and network science. His work combines theoretical and computational approaches to understand how structure and randomness influence the behaviour of biological and social systems.

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. His research interests include dynamical systems, partial differential equations and their applications in chemistry and biology. His work focuses on the modeling and analysis of network processes using differential equations.