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; Selected answers; Author index; Subject index.
This book is an introduction for readers interested in biological applications of mathematics and modeling in biology, showing how relatively simple mathematics can be applied to a variety of models. Despite the great advances that have taken place, the simple lessons described in the text are still important and informative.
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