Mathematics of Epidemics on Networks

This textbook offers a distinctive and rigorous introduction to network-based epidemic modelling, providing a clear and methodical link between models and their mathematical foundations. Sitting at the interface of epidemiology, graph theory, stochastic processes, and dynamical systems, the second edition expands from 11 to 15 chapters with new coverage of stochastic models, statistical inference, simple and complex contagions, and higher-order network structures. The book incorporates recent theoretical advances while retaining the unified mathematical framework that defined the first edition. The authors aim to close the gap between epidemic models and the mathematics that underpin them by: Presenting the state of the art in modelling epidemics on networks, with results and ready-to-use models highlighted throughout; Introducing multiple mathematical approaches--including stochastic formulations--to derive exact and approximate models; Clarifying how approximate models relate to their rigorous mathematical representations; Providing a coherent model hierarchy that links assumptions to model complexity; Introducing likelihood-based and Bayesian inference tools for parameter estimation from epidemic data; Extending classical models to higher-order interactions and complex contagion processes; Serving as a comprehensive reference for advanced undergraduates, graduate students, and researchers; Supplying software for solving differential-equation models and simulating network-based epidemics. Rich with diagrams, examples, exercises, and online simulation code, the book is accessible to students with varied mathematical backgrounds and suitable for advanced undergraduate and graduate courses across mathematics and related disciplines.