Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community since its first publication in 1988, the book shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in Mathematical Models in Biology are still important and informative. Shortly after the first publication of Mathematical Models in Biology, the genomics revolution turned Mathematical Biology into a prominent area of interdisciplinary research. In this new millennium, biologists have discovered that mathematics is not only useful, but indispensable! As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called mathematical biology. This book serves as a basic introduction to concepts in deterministic biological modeling.
Leah Edelstein-Keshet is a member of the Mathematics Department at the University of British Columbia and past president of the Society for Mathematical Biology. She has been involved in research in mathematical biology for over 30 years, most recently as a team leader of a Mathematics of Information Technology and Complex Systems MITACS (Canada) biomedical modeling team.
Acknowledgments Part 1: Discrete Process in Biology Chapter 1: The Theory of Linear Difference Equations Applied to Population Growth Chapter 2: Nonlinear Difference Equations Chapter 3: Applications of Nonlinear Difference Equations to Population Biology Part 2: Continuous Processes and Ordinary Differential Equations Chapter 4: An Introduction to Continuous Models Chapter 5: Phase-Plane Methods and Qualitative Solutions Chapter 6: Applications of Continuous Models to Population Dynamics Chapter 7: Models for Molecular Events Chapter 8: Limit Cycles, Oscillations, and Excitable Systems Part 3: Spatially Distributed Systems and Partial Differential Equation Models Chapter 9: An Introduction to Partial Differential Equations and Diffusion in Biological Settings Chapter 10: Partial Differential Equation Models in Biology Chapter 11: Models for Development and Pattern Formation in Biological Systems Selected Answers Author Index Subject Index
