Biomathematics is the use of mathematical models to help understand phenomena in biology. Modern experimental biology is very good at taking biological systems apart (at all levels of organization, from genome to global nutrient cycling), into components simple enough that their structure and function can be studied in isolation. Dynamic models are a way to put the pieces back together, with equations that represent the system’s components, processes, and the structure of their interactions.
Mathematical models are important tools in basic scientific research in many areas of biology, including physiology, ecology, evolution, toxicology, immunology, natural resource management, and conservation biology. The result obtained from analysis and simulation of system models are used to test and extend biological theory, and to suggest new hypotheses or experiments. Models are also widely used to synthesize available information and provide quantitative answers to practical questions. What measures can be used to reverse the decline in sea turtle populations, and how soon can we tell if they are working? How can laboratory experiments on chemical carcinogenicity be scaled up to set safe exposure limits on humans? For questions like these, where it is desirable to predict the outcome accurately before action is taken, quantitative modeling is essential.
Thus, while mathematical biology may sound like a narrow discipline, in fact it encompasses all of biology and virtually all of the mathematical sciences, including statistics, operations research, and scientific computing.
Within the biomathematics program at Illinois State, faculty and student research areas include artificial intelligent modeling, evolutionary computing, infectious disease modeling, ecology, gene regulatory networks, agent-based models. Thanks to the Intercollegiate Biomathematics Alliance, students also have access to unprecedented nationwide expertise.
Research on specific applications is complemented by fundamental work on mathematical, statistical, and computational methods for fitting models to data and deriving their properties. The research interests of biomathematics faculty and current students are described elsewhere on this website.
A good place to get an idea of what mathematical modeling is all about is an article by Jackson et al. (2000) that appeared in the journal BioScience, volume 50, issue number 8, pages 694–706. Another good place to look is the February 6th, 2004 edition of the journal Science (volume 303) which contains a series of articles on various areas of mathematical biology.