System for modeling the spatial dynamics of the bacterial population under varying antimicrobial treatment regimes

This work is devoted to the development and implementation of a model for the evolution of a bacterial population grown on a nutrient medium under conditions of controlled biomass inhibition by an antimicrobial agent. To formalize the model a continuous deterministic approach is used. The mathematical model is described by an initial boundary value problem for a system of reaction-diffusion equations defining the spatio-temporal distributions of nutrient substrate and biomass, taking into account integration with a pharmacokinetic model for a single antimicrobial treatment. The model was implemented by the finite element method using the finite element analysis system – COMSOL Multiphysics platform. A series of computational experiments were performed to establish numerical patterns of changes in bacterial mass concentration with variation in antimicrobial dose. A discussion of the potential application of this approach to investigate the issue of bacterial resistance to antibiotics is presented.

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