Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. Connections are made between diverse biological examples linked by common mathematical themes, exploring a variety of discrete and continuous ordinary and partial differential equation models. 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.
Part I. Discrete Process in Biology
1. The theory of linear difference equations applied to population growth
2. Nonlinear difference equations
3. Applications of nonlinear difference equations to population biology
Part II. Continuous Processes and Ordinary Differential Equations
4. An introduction to continuous models
5. Phase-plane methods and qualitative solutions
6. Applications of continuous models to population dynamics
7. Models for molecular events
8. Limit cycles, oscillations, and excitable systems
Part III. Spatially Distributed Systems and Partial Differential Equation Models
9. An introduction to partial differential equations and diffusion in biological settings
10. Partial differential equation models in biology
11. Models for development and pattern formation in biological systems
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.