Princeton Series in Theoretical and Computational Biology

Odo Diekmann is professor of mathematical analysis at Utrecht University. Hans Heesterbeek is professor of theoretical epidemiology at Utrecht University. Tom Britton is professor of mathematical statistics at Stockholm University. Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. • Covers the latest research in mathematical modeling of infectious disease epidemiology • Integrates deterministic and stochastic approaches • Teaches skills in model construction, analysis, inference, and interpretation • Features numerous exercises and their detailed elaborations • Motivated by real-world applications throughout "A much needed book. Mathematical Tools for Understanding Infectious Disease Dynamics is a welcome addition to the current literature and will hopefully help to unify the many different views in the field."---Laura Matrajt, SIAM Review "The overtly pedagogical features of this text make it an outstanding choice for someone trying to learn the basic tools of the trade. The mathematician who makes a serious study of this text will be in an excellent position to work fruitfully with biologists or epidemiologists on either theoretical or data-driven problems of disease transmission."---Carl A. Toews, Mathematical Reviews "This book will soon be a classic in the theoretical epidemiology and modeling literature."---Mirjam Kretzschmar, Biometrical Journal "This landmark volume describes for readers how one should view the theoretical side of mathematical epidemiology as a whole. A particularly important need is for a book that integrates deterministic and stochastic epidemiological models, and this is the first one that does this. I know of no better overview of the subject. It belongs on the shelf of everyone working in mathematical epidemiology."-Fred Brauer, University of British Columbia

Volker Grimm is a Senior Researcher at the UFZ Centre for Environmental Research Leipzig-Halle and Lecturer at the University of Potsdam. Steven F. Railsback is a consulting scientist and Adjunct Professor of Mathematics at Humboldt State University. Individual-based models are an exciting and widely used new tool for ecology. These computational models allow scientists to explore the mechanisms through which population and ecosystem ecology arises from how individuals interact with each other and their environment. This book provides the first in-depth treatment of individual-based modeling and its use to develop theoretical understanding of how ecological systems work, an approach the authors call "individual-based ecology.? Grimm and Railsback start with a general primer on modeling: how to design models that are as simple as possible while still allowing specific problems to be solved, and how to move efficiently through a cycle of pattern-oriented model design, implementation, and analysis. Next, they address the problems of theory and conceptual framework for individual-based ecology: What is "theory"? That is, how do we develop reusable models of how system dynamics arise from characteristics of individuals? What conceptual framework do we use when the classical differential equation framework no longer applies? An extensive review illustrates the ecological problems that have been addressed with individual-based models. The authors then identify how the mechanics of building and using individual-based models differ from those of traditional science, and provide guidance on formulating, programming, and analyzing models. This book will be helpful to ecologists interested in modeling, and to other scientists interested in agent-based modeling. "The authors establish an effective and coherent framework for using individual-based modelling."---Nikita Y. Ratanov, Mathematical Reviews "An excellent book, which aims to invigorate individual-based modeling . . . by providing a clear theoretical framework for the subject--which they term individual-based ecology (IBE)--and a step-by-step guide to creating individual-based models (IBMs) within this framework. . . . I think this is a very timely book, and I recommend it to anyone new or old to the subject."---Richard Stillman, Quarterly Review of Biology "The book very successfully link[s] various 'universes' ranging from fundamental concepts in ecology and complex systems research to hands-on technical and recipe-like suggestions on how to build a model, illustrated with numerous, well-chosen examples."---Janine Bolliger, Landscape Ecology "For anyone who wants to know more about and possibly incorporate IBMs in his own research, this book provides plenty of advice and guidance on how to formulate, analyze, and use such models. If IBMs do ultimately reach the potential envisioned by the authors, their seminal book will have done much to contribute to that success."---Jim M. Cushing, Zentralblatt MATH "This book establishes an effective and coherent conceptual and technical framework for individual-based modeling with the objective to develop and illustrate an approach for addressing how individual behaviors and system dynamics emerge from lower-level traits."---Janine Bolliger, Landscape Ecology "Given the solid conceptual foundation of the book and the wide range of IBM applications in fish ecology, I think that many fish biologists will find this book very useful and I recommend it warmly."---Geir Huse, Fish and Fisheries "This seminal book truly deserves to be called the founding text for the growing field of individual-based modeling and the broader program of individual-based ecology. Core procedures and standards for formulating, parameterizing, testing, and communicating such models have long been lacking. Even the basic definitions have been missing. In one stroke, Grimm and Railsback provide all of those things. Thus, individual-based modeling now has a founda

Freddy Bugge Christiansen is professor of population biology at the University of Aarhus in Denmark. He is the author of Population Genetics of Multiple Loci and coauthor of Theories of Populations in Biological Communities and Population Genetics. This textbook provides an authoritative introduction to both classical and coalescent approaches to population genetics. Written for graduate students and advanced undergraduates by one of the world's leading authorities in the field, the book focuses on the theoretical background of population genetics, while emphasizing the close interplay between theory and empiricism. Traditional topics such as genetic and phenotypic variation, mutation, migration, and linkage are covered and advanced by contemporary coalescent theory, which describes the genealogy of genes in a population, ultimately connecting them to a single common ancestor. Effects of selection, particularly genomic effects, are discussed with reference to molecular genetic variation. The book is designed for students of population genetics, bioinformatics, evolutionary biology, molecular evolution, and theoretical biology--as well as biologists, molecular biologists, breeders, biomathematicians, and biostatisticians. • Contains up-to-date treatment of key areas in classical and modern theoretical population genetics • Provides in-depth coverage of coalescent theory • Discusses genomic effects of selection • Gives examples from empirical population genetics • Incorporates figures, diagrams, and boxed features throughout • Includes end-of-chapter exercises • Speaks to a wide range of students in biology, bioinformatics, and biostatistics "This very well-written book is challenging, but rewarding. Motivated readers will understand the dynamic nature of genetic variation in populations."---Richard M. Kijman, Quarterly Review of Biology "I applaud the primary goal of this book, that is, to present basic genetic and population genetic concepts to future researchers in genomics and bioinformatics. I think that understanding the core evolutionary framework is essential for successful analysis and interpretation of contemporary genetic data."---Phil Hedrick, Journal of Heredity