# A MATHEMATICAL MODEL OF THE WAY MICROORGANISMS REPRODUCE AT THE EXPENSE OF NUTRIENT CONSUMPTION IN THE CHEMOSTAT

## Abstract

One of the simplest experiments in microbiology is the growing unicellular microorganisms such as bacteria and following changes in their population over a period of time. We discuss the mathematical representation of such an experiment as modeled by [1] (for equations see 'Additional Files' below) where *N(t)* represents the density of the microorganism, *C(t)* is the concentration of the stock nutrient, C_{0 }is the initial concentration, *K*_{max }represents an upper bound for *K(C)*, and for C = K_{n}, K(C) = (1/2)*K*_{max} , *µ* is the mortality rate of the microorganism, while *D* and α are rate parameters. We use dimensional analysis to reduce the number of parameters and also calculate the steady states and investigate their linear stability properties. [1] G.F Gause, *The Struggle for Existence*. (Hafner Publishing, New York, 1969).

## Recommended Citation

Oyedeji, Kale
(2017)
"A MATHEMATICAL MODEL OF THE WAY MICROORGANISMS REPRODUCE AT THE EXPENSE OF NUTRIENT CONSUMPTION IN THE CHEMOSTAT,"
*Georgia Journal of Science*, Vol. 75, No. 1, Article 79.

Available at:
https://digitalcommons.gaacademy.org/gjs/vol75/iss1/79