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Home  >  Volume 46 (May, 2018)

15. MATHEMATICAL MODEL OF BACTERIA-NUTRIENT HARVESTING IN A CULTURED ENVIRONMENT by Udofia Ekere Sunday, Amos Amos Idungafa Volume 46 (May, 2018 Issue), pp115 –118
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MATHEMATICAL MODEL OF BACTERIA-NUTRIENT HARVESTING IN A 

CULTURED ENVIRONMENT

Udofia Ekere Sunday1, Amos Amos Idungafa2

Department of Mathematics and Statistics1, Akwa Ibom State University, Ikot Akpaden,

Akwa Ibom State, Nigeria.

Department of Physics2, Akwa Ibom State University, Ikot Akpaden, Akwa Ibom State, Nigeria.

Abstract

In this paper, we develop mathematical model of bacteria-nutrient harvesting in a cultured environment. This model which assumes that the rate of harvesting of these bacteria is constant results in a system of first order differential equations. Analyzing the model, it was discovered that the product of the maximum nutrient uptake per cell and the number of cells produced per unit of nutrient uptake is constant(VY   =   ln2 +h).

It was also assumed that the rate of harvesting of these bacteria varies and a corresponding model was developed. Analyzing this model using methods from dynamical systems theory, it was seen that the system has two steady states. The first steady state is unstable while the second is globally asymptotically stable if the carrying capacity of the environment has a lower bound, which is a ratio of the harvesting coefficient of the bacteria, cost per unit effort per unit price of the bacteria.

Keywords: Bacteria, Dynamical Systems, Steady State, Cultured Environment, Variable Effort

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