The Network Science Institute is proud to announce the publication of the second edition of Mathematics of Epidemics on Networks: From Exact to Approximate Models, co-authored by the NetSI London faculty member Prof. István Kiss.
Nine years after the first edition, the intent of the book—which has since been cited more than 900 times—remains unchanged: to provide a unified mathematical framework that bridges different modeling approaches while remaining accessible to researchers from diverse backgrounds. In their preface, however, the authors explain the need for an expanded and updated version to keep pace with the rapid developments in the field. The COVID-19 pandemic, in particular, renewed attention to mathematical epidemiology and exposed both the strengths and the limits of network-based models; while newer developments, such as higher-order networks, opened directions the original book could not have anticipated.
What has changed
Chapters 1 through 6 map onto the first edition but have been harmonized and updated throughout, adding a mean-field model based on survival-theory, a fast variable approach to correlations and the epidemic threshold, pairwise models with clustering, and exact closures for particular networks and dynamics. Four chapters are entirely new.
- Chapter 7, "Simple and Complex Contagions," extends the book's models to other contagious processes, including the adoption of new beliefs or technologies.
- Chapter 8,"Higher-Order Contagion Models," carries the same pairwise philosophy into hypergraphs and simplicial complexes, working through both top-down and bottom-up derivations of the resulting mean-field equations.
- Chapter 10,"Stochastic Trajectory Models," models individual-level transmission using continuous-time, discrete-space Markov chains, supporting Gillespie-style simulation and, in turn, likelihood-based inference.
- Chapter 11, "Survival Models and Statistical Inference," builds on that stochastic view to develop a Bayesian inference framework, illustrated with data from the2018–2020 Ebola outbreak.
Chapters 12 through 15 carry forward and update the material from the first edition's Chapters 8 through 11.
The Epidemics on Networks (EoN) Python package, which grew out of the first edition's appendix on simulation algorithms, has become widely used in its own right and continues to be maintained; it was used to generate many of this edition's figures, with the corresponding code provided in its documentation. The book keeps the diagrams, worked examples, and exercises that made the first edition usable by readers with or without a strong mathematics background, extending them to the new material.
About the book
Sitting at the interface of epidemiology, graph theory, stochastic processes, and dynamical systems, this textbook is a contribution to network science. It offers a stronger and more methodical link of models to their mathematical origin, and explains how those models relate to one another with a particular focus on epidemic spread on networks. It is written as a reference for advanced undergraduates, doctoral students, postdoctoral researchers, and academic experts working on stochastic processes on networks, and it comes with software for solving differential equation models or simulating epidemics on networks directly.
