A MATHEMATICAL MODELING OF MICROBIAL GROWTH IN A CHEMOSTAT SUBMITTED TO THE DEPARTMENT OF MATHEMATICS IN PARTIALFULFILLMENT OF THE REQIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MATHEMATICS

Abstract

This study presents a mathematical model for the dynamics of microbial growth in a chemostat, a bioreactor designed for a continuous nutrient supply and microorganism culture. The model utilizes a set of differential equations to depict the interaction between microbial biomass and limiting nutrient concentrations, employing the Monod equation to describe growth kinetics. Key parameters such as the maximum specific growth rate, half –saturation constant, and yield coefficient are incorporate to characterize the biological processes accurately. The model comprises two primary equations, one governing the change in microbial population density and another capturing substrate consumption dynamics. By analyzing the model, we gain insights into the effects of dilution rates nutrient input on microbial growth, which can inform optimal operational strategies for maximizing biomass production. Simulations demonstrate the models utility in predicting steady state conditions and transient dynamics, thus providing a valuable tool for researchers and engineers in designing efficient bioreactor systems. This mathematical framework not only enhances our understanding of microbial ecology in controlled environments but also contributes to advancements in applied microbiology and biotechnology. There are many types of bioreactors used for producing microbial growth in commercial, medical and research applications. The most important models corresponding to the well-known reproduction kinetics such as the Michaelis-Menten kinetics, competitive substrate inhibition and competitive product inhibition.The analysis involves equilibrium and stability analysis using linearization techniques and eigen value evaluation as well as sensitivity analysis to examine the influence of key parameters such as dilution rate, maximum growth rate, and substrate concentration. MATLAB solver was used to simulate the model numerically. The major results of the study show that the chemostat system admits both washout and positive equilibrium states depending on the operating parameters.