This book covers recent developments in epidemic process models and related data on temporally varying networks. It is widely recognized that contact networks are indispensable for describing, understanding, and intervening to stop the spread of infectious diseases in human and animal populations; “network epidemiology” is an umbrella term to describe this research field. More recently, contact networks have been recognized as being highly dynamic. This observation, also supported by an increasing amount of new data, has led to research on temporal networks, a rapidly growing area. Changes in network structure are often informed by epidemic (or other) dynamics, in which case they are referred to as adaptive networks. This volume gathers contributions by prominent authors working in temporal and adaptive network epidemiology, a field essential to understanding infectious diseases in real society.

The concept of temporal networks is an extension of complex networks as a modeling framework to include information on when interactions between nodes happen. Many studies of the last decade examine how the static network structure affect dynamic systems on the network. In this traditional approach the temporal aspects are pre-encoded in the dynamic system model. Temporal-network methods, on the other hand, lift the temporal information from the level of system dynamics to the mathematical representation of the contact network itself. This framework becomes particularly useful for cases where there is a lot of structure and heterogeneity both in the timings of interaction events and the network topology. The advantage compared to common static network approaches is the ability to design more accurate models in order to explain and predict large-scale dynamic phenomena (such as, e.g., epidemic outbreaks and other spreading phenomena). On the other hand, temporal network methods are mathematically and conceptually more challenging. This book is intended as a first introduction and state-of-the art overview of this rapidly emerging field.

This book focuses on the theoretical side of temporal network research and gives an overview of the state of the art in the field. Curated by two pioneers in the field who have helped to shape it, the book contains contributions from many leading researchers. Temporal networks fill the border area between network science and time-series analysis and are relevant for epidemic modeling, optimization of transportation and logistics, as well as understanding biological phenomena. Over the past 20 years, network theory has proven to be one of the most powerful tools for studying and analyzing complex systems. Temporal network theory is perhaps the most recent significant development in the field in recent years, with direct applications to many of the “big data” sets. This book appeals to students, researchers, and professionals interested in theory and temporal networks—a field that has grown tremendously over the last decade. This second edition of Temporal Network Theory extends the first with three chapters highlighting recent developments in the interface with machine learning.

Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological StudiesSpatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and

Network science offers a powerful language to represent and study complex systems composed of interacting elements — from the Internet to social and biological systems. A Guide to Temporal Networks presents recent theoretical and modelling progress in the emerging field of temporally varying networks and provides connections between the different areas of knowledge required to address this multi-disciplinary subject. After an introduction to key concepts on networks and stochastic dynamics, the authors guide the reader through a coherent selection of mathematical and computational tools for network dynamics. Perfect for students and professionals, this book is a gateway to an active field of research developing between the disciplines of applied mathematics, physics and computer science, with applications in others including social sciences, neuroscience and biology.This second edition extensively expands upon the coverage of the first edition as the authors expertly present recent theoretical and modelling progress in the emerging field of temporal networks, providing the keys to (and connections between) the different areas of knowledge required to address this multi-disciplinary problem.

This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.

In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.

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. 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.

This innovative textbook brings together modern concepts in mathematical epidemiology, computational modeling, physics-based simulation, data science, and machine learning to understand one of the most significant problems of our current time, the outbreak dynamics and outbreak control of COVID-19. It teaches the relevant tools to model and simulate nonlinear dynamic systems in view of a global pandemic that is acutely relevant to human health. If you are a student, educator, basic scientist, or medical researcher in the natural or social sciences, or someone passionate about big data and human health: This book is for you! It serves as a textbook for undergraduates and graduate students, and a monograph for researchers and scientists. It can be used in the mathematical life sciences suitable for courses in applied mathematics, biomedical engineering, biostatistics, computer science, data science, epidemiology, health sciences, machine learning, mathematical biology, numerical methods, and probabilistic programming. This book is a personal reflection on the role of data-driven modeling during the COVID-19 pandemic, motivated by the curiosity to understand it.

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).