The Evolution Model of Cultured Bacteria with External Growth Inhibition: Computational Techniques and in silico Studies

Microbiological systems have become relevant objects of interdisciplinary research in mathematical biology and bioinformatics and can be analyzed using in silico studies with the implementation of computational experiments. The design of mathematical models of bacterial biomass growth under external inhibition can help to predict states of the microbiological system, reduce antibiotic use, and avoid antimicrobial resistance. The paper is devoted to developing a mathematical model of nutrient-dependent dynamics of bacteria cultured in media, considering external surface growth inhibition. The mathematical problem statement includes governing equations to define spatial-temporal distributions of bacterial biomass concentration, nutrient concentration, and time-dependent dose of antibiotic concentration. We propose a joint numerical scheme based on finite difference methods and specialized program application implemented with Matlab. A series of computational experiments were performed to describe the distributions of the key chemical compounds characterizing bacterial surface growth exposed to antibiotics and predict antibiotic treatment strategies.