Study of Microorganism Growth Kinetics Based on Mono's Mathematical Model

• Date: 2026
• Main Authors: Радзієвська, Олена, Ковальська, Ірина
• Format: Article
• Language: Ukrainian
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Online Access: https://mcm-math.kpnu.edu.ua/article/view/360132
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

Mathematical modelling of microbial growth is a cornerstone of modern biotechnology, industrial microbiology, and systems biology. It allows not only to describe observed phenomena, but also to predict the behaviour of populations in response to environmental changes, which is critically important for optimizing the yield of target products, designing bioreactors, and controlling wastewater treatment processes. The basis of bioprocess engineering is the transformation of biological mechanisms into a system of quantitative equations that reflect the interaction between a cell and its environment. The development of this direction began with the empirical observations of Jacques Monod, who in the middle of the 20th century established a fundamental analogy between the growth rate of whole microbial cells and the kinetics of Michaelis-Menten enzymatic reactions. Since then, modelling has evolved from simple unstructured descriptions to complex segregated and stochastic approaches that take into account intracellular regulation and population heterogeneity. This article investigates the kinetics of microbial growth based on the Mono mathematical model, which reveals the dependence of the growth rate of a batch culture on the concentration of the substrate (nutrient). This model is described by a system of differential equations. The dependence of the concentration of microorganisms on time is studied under given initial conditions. The disadvantage of this model is that the dependence of the concentration on time cannot be written explicitly. However, by studying the solution, this dependence can be described and plotted.