Mathematical Models in the Sciences

Abstract

A mathematical model is an attempt to describe a natural phenomenon quantitatively. Mathematical models in the molecular biosciences appear in a variety of ways: some models are deterministic while others are stochastic, some models regard time as a discrete quantity while others treat it as a continuous variable, and some models offer algebraic relationships between variables while others describe how those variables evolve over time. This entry begins with a coarse dichotomy ofsome of the most common types of mathematical models. As an illustration, two very different models of the same simple decay process are derived and contrasted. The entry concludes with a discussion of (i) limitations of mathematical models, (ii) validation of models against scientific data, and (iii) the iterative process of refining and improving a model.