Mathematics of Epidemics on Networks

Beschreibung

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.

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.

Autor*in

István Z. Kiss

Themen in »Mathematics of Epidemics on Networks«

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

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