Mathematical Models in Microbiology

Abstract

With the development of accurate measurement techniques, there is a growing need for interpretation of quantitative data in microbiology. However, biological systems are by nature extremely complex and the actual system has to be replaced by an imaginary model system, which is mathematically tractable. The model system is arrived at by making simplifying assumptions and generalizations about the nature of the microbiological system. The results of the mathematical analysis are applicable only to the model system. The applicability of the results to the biological system depends on the validity of the assumptions. This chapter discusses the underlying principles used in the formulation of mathematical models and presents some simple aids to mathematical analysis of models. While models have serious drawbacks, they can be useful tools when their limitations are fully understood. Construction of such models provides a systematic way of studying behavior of specific systems for which experimental data are available. This approach encourages the microbiologist to be rigorous in his statements and definitions. Realistic and tested models provide useful guides for design and operation of industrial microbiological processes. In research, models can be used as conceptual tools to gain insight into biological mechanisms. They can be used to predict behavior in some untested situation or to test the plausibility of various suggested mechanisms. This approach often points to a critical region where further experiments should be carried out. © 1973, Academic Press Inc.