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Mathematical Tools for Understanding Infectious Disease Dynamics
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 statist...
Delay Equations
The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.
Mathematics for Ecology and Environmental Sciences
This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.
Mathematical Epidemiology of Infectious Diseases
Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are un...
Functional Analysis and Evolution Equations
Gunter Lumer was an outstanding mathematician whose works have great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips from 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Gunter Lumer.
Epidemic Models
Surveys the state of epidemic modelling, resulting from the NATO Advanced Workshop at the Newton Institute in 1993.
Spaces of Measures and their Applications to Structured Population Models
Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.
Analysis of Evolutionary Processes
Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. In Analysis of Evolutionary Processes, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics. After introducing the basics of evolutionary processes and classifying available modeling approac...
Introduction to Reaction-Diffusion Equations
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the sprea...
Temporal Network Epidemiology
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.
