ABSTRACT
I. Introduction 302II. General Mathematical Biology 303A. Undergraduate/introductory texts 303B. Advanced general sources 305C. Major journals, book series, and conferences 306D. Databases and internet resources 308III. Population Biology 309A. Population dynamics 309B. Demographics 309C. Ecology 310IV. Genetics and Evolution 313V. Epidemiology 314VI. Computational Biology, Bioinformatics 316VII. Physiology 318A. Modeling of organs and body systems 318B. Neural biology 320C. Biochemistry, kinetics in biochemical problems 322VIII. Medical Applications 323IX. Selected Topics 323A. Animal behavior 323 301
B. Biophysics, biomechanics, biological fluid mechanicsC. MorphologyD. Cell biology and cell movement 324324325
Mathematical biology is a rapidly growing subdiscipline of mathematics. Interest in applying mathematical tools to biological phenomena goes back to the beginning of the twentieth century when population models were introduced to understand disease dynamics, predator-prey interactions, and competition between species. The field has broadened enormously since then, comprising biological phenomena from molecules to ecosystems. Examples include gene flow in agricultural or natural systems, gene regulation networks, cell movement, neuron activity, tumor growth, morphogenesis, immunology, population dynamics in fragmented habitats, nutrient cycling in aquatic or terrestrial systems, and many others.Models in biology are phenomenological, empirical, or mechanistic, depending on their purpose. They can be explanatory or predictive. Mathematical models are often formulated as difference or differential equations, whose analysis require both analytical and numerical techniques. Probabilistic models are increasingly important, in particular in the emerging fields of molecular biology. Additionally, simulation models are often used for more detailed, data-driven modeling.Mathematical biology is highly interdisciplinary. It requires a diverse array of mathematical tools, but also knowledge of the underlying biological system. A researcher in this field must therefore not only gain a broad mathematical foundation but also sufficient biological knowledge to contribute to both the mathematical and the biological discipline. Close collaboration with biologists is often essential to achieve this goal.This chapter concentrates on modern research areas and methods, with occasional mentions of works that were very influential in their time and that are helpful for understanding how the field developed. In addition to the resources specifically recommended here, more information about relevant mathematical theory and techniques is available in the chapters covering partial differential equations, numerical analysis, probability theory and stochastic processes, and combinatorics (especially graph theory).
