Mathematics of Epidemics on Networks
From Exact to Approximate Models
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Beschreibung
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.
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 differential equation models or directly simulate epidemics on networks.
Details the current state-of-the-art in modeling epidemics on networks Offers direct comparison of the main network epidemic models and works out their hierarchy Identifies opportunities for further rigorous mathematical exploration Features practical simulation algorithms written in pseudocode with implemented code available online Includes supplementary material: sn.pub/extras
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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“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)
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