Mathematical model of the bacteria-nutrient dynamics

Abstract

In this paper we developed a Mathematical Model of bacteria-nutrient dynamics which results in a system of first order ordinary differential equations. The analysis of the model was done using dynamical systems. It was found out that the product of the maximum nutrient uptake per cel; and the number of cells produced per unit of nutrient uptake is a constant (VY = In 2). It is also shown that there is a linear relationship between the concentration of the limiting nutrients and number of bacteria with a negative slope. It is finally shown that after a long time, the number of bacterial will be a constant and will depend on the initial concentration of the nutrient and the initial number of bacterial.

JONAMP Vol. 11 2007: pp. 145-148