商品描述
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.
商品描述(中文翻譯)
這本教科書為網路科學領域提供了一個令人興奮的新補充，強調模型與其數學起源之間更強且更有系統的連結，並解釋這些模型之間的關係，特別關注於網路上的疫情擴散。書中的內容位於流行病學、圖論、隨機過程和動態系統的交界處。這第二版從11章擴展到15章，增加了對隨機模型、統計推斷、簡單和複雜傳染以及高階網路結構的全面覆蓋。新材料反映了最近的理論進展，同時保持了使第一版如此有價值的統一數學框架。作者旨在為縮小模型開發與支持數學之間的差距做出重要貢獻。這是通過以下方式實現的：
- 總結並呈現網路上疫情建模的最新技術，並在全書中標示出結果和可直接使用的模型；
- 提出不同的數學方法，包括隨機模型，以制定精確且可解的模型；
- 確定近似模型與其嚴謹數學表示之間的具體聯繫；
- 呈現模型層級，並清楚地突出模型假設與模型複雜性之間的聯繫；
- 介紹基於似然的推斷框架和貝葉斯工具，用於從實際疫情數據中進行參數估計；
- 將經典的網路疫情模型擴展到高階結構和複雜傳染過程；
- 為高年級本科生、博士生、博士後研究人員及從事網路上隨機過程建模的學術專家提供參考資料；
- 提供可以解決微分方程模型或直接模擬網路上疫情的軟體。
這本書充滿了大量的圖表、範例、指導性練習，以及在線訪問模擬算法和可直接使用的代碼，將吸引來自不同背景和學術水平的廣泛讀者。適合具有或不具有強大數學背景的學生，這本教科書可以作為數學及其他學科的高年級本科或研究生課程的基礎。
作者簡介
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.
作者簡介(中文翻譯)
I.Z. Kiss: Kiss教授是倫敦東北大學網絡科學研究所的網絡科學教授，他的研究位於流行病學、網絡科學、隨機過程和動態系統的交界處。他的工作專注於靜態、動態和高階網絡上隨機過程的建模和分析。他的研究結合了數學深度與實際影響，推進了從公共健康到技術等領域的基本理解和應用解決方案。
J.C. Miller: Miller副教授是墨爾本拉籌伯大學數學與物理科學系的副教授，也是澳大利亞醫療創新人工智慧中心的成員。此前，他曾是西雅圖疾病建模研究所的高級研究科學家。他的研究興趣包括傳染病的動態、網絡上的隨機過程，以及隨機模擬的算法開發。
G.A. Rempala: Rempala教授是美國俄亥俄州立大學的生物統計學和數學教授。他的研究位於應用概率、隨機過程和數學生物學的交界處。他特別對流行病學和網絡科學中出現的複雜動態系統的建模和分析感興趣。他的工作結合了理論和計算方法，以理解結構和隨機性如何影響生物和社會系統的行為。
P.L. Simon: Simon教授是布達佩斯厄爾特大學數學研究所的教授。他是數值分析和大型網絡研究小組的成員。他的研究興趣包括動態系統、偏微分方程及其在化學和生物學中的應用。他的工作專注於使用微分方程對網絡過程進行建模和分析。
