Mathematical Models in Population Biology and Epidemiology

This textbook provides an introduction to the field of mathematical biology through the integration of classical applications in ecology with more recent applications to epidemiology, particularly in the context of spread of infectious diseases. It integrates modeling, mathematics, and applications in a semi-rigorous way, stating theoretical results and giving references but not necessarily giving detailed proofs, providing a solid introduction to the field to undergraduates (junior and senior level), graduate students in applied mathematics, ecology, epidemiology or evolutionary biology, sustainability scientists, and to researchers who must routinely read the practical and theoretical results that come from modeling in ecology and epidemiology.

This new edition has been updated throughout. In particular the chapters on epidemiology have been updated and extended considerably, and there is a new chapter on spatially structured populations that incorporates dispersal.The number of problems has been increased and the number of projects has more than doubled, in particular those stressing connections to data. In addition some examples, exercises, and projects include use of Maple and Matlab.

Review of first edition:

"A strength of the book is the large number of biologically-motivated problem sets. These and the references to the original biological papers would be valuable resources for an instructor." (UK Nonlinear News, 2001)

Auteur

Fred Brauer, Department of Mathematics, University of British Columbia, Canada; Carlos Castillo-Chavez, Mathematical, Computational and Modeling Sciences Center, Arizona State University, USA

Texte du rabat

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

Contenu

Preface Ackn. Prologue Part I: Simple Single-Species Models 1 Continuous Population Models 2 Discrete Population Models 3 Continuous single-species Population Models with Delays Part II: Models for Interacting Species 4 Introduction and Mathematical Preliminaries 5 Continuous models for two interacting populations 6 Harvesting in two-species models Part III: Structured Population Models 7 Basic ideas of Mathematical Epidemiology 8 Models for population with age structure Epilogue Answers to selected Exercises References