ABSTRACT

Mathematical modeling has been used to explain biological systems for centuries, going back to work such as that of Thomas Malthus (1798) on the growth of populations, Daniel Bernouilli (1760) on smallpox vaccination and arguably Fibonacci (Leonardo of Pisa, 1202) on the well-known rabbit problem. Modern mathematical biology has been an ongoing scientific endeavor since the end of the nineteenth century, growing out of the work of individuals such as P.D. En’ko in epidemiology, D’Arcy Wentworth Thompson in change in biological organisms, and G. Stokes in fluid flows, and the technical developments of the late twentieth century have placed it in the forefront of scientific research. The use of theoretical models to describe and predict the behavior of biological systems is especially useful today in examining large-scale questions where controlled experiments are either impossible or unethical to carry out — the effects of large-scale alterations in environmental conditions on local ecology, or of slight decreases in efficiency of certain disease control measures. Even in situations where some experimental data is available, mathematical models may validate existing theories or provide new insights by describing the mechanisms through which biological processes occur, taking in a whole spectrum of possible measurements in a single step. More specifically, one might use modeling

• to predict unknown behavior (such as intervention effects) based on given factors,

• to generate virtual experiments that inform general biological theory, • to account for observed behavior as simply as possible, • to compare competing hypotheses — which better accounts for observed results?