Identification of mathematical model of bacteria population under the antibiotic influence

A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment. We consider a non-linear PDE model of biofilm growth subject to initial and Dirichlet boundary conditions, and the inverse coefficient problem of recovering the unknown parameters in the model from extra measurements of quantities related to the biofilm and substrate. By addressing and analysing this inverse problem we provide reliable and robust reconstructions of the primary physical quantities of interest represented by the diffusion coefficients of substrate and biofilm, the biomass spreading parameters, the maximum specific consumption and growth rates, the biofilm decay rate and the half saturation constant. We give particular attention to the constant coefficients involved in the leading-part non-linearity, and present a uniqueness proof and some numerical results. In the course of the numerical investigation, we have identified extra data information that enables improving the reconstruction of the eight-parameter set of physical quantities associated to the model of biofilm growth.

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Inverse problems for a model of biofilm growth

Brander

Lesnic

Cao

2023

IMA Journal of Applied Mathematics

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Teaching High School Students to Solve Differential Equations Using Python at Math Class

Alkhan

Shaimova²

2020

Bullet. Ser. of Phys. & Math. Sc.

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The article discusses examples of the differential equation problem in Python with a graph for high school students. The basic characteristics of some tools for solving problems in mathematics using information technology are given. The difference between the two modern-known computer programs Python and Pascal is briefly explained. The article uses illustrative examples of built-in and manually entered functions that can be repeated by readers in Python to recreate graphs of trigonometric, differential, and other functions. In conclusion, it describes how the program can save time and energy for solving graphic problems in mathematics using the Python program. The article concludes that it is important for students to use logic to solve problems with improvised tools, where there are built-in functions, compared to remembering programming language algorithms for solving problems.

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Identification of mathematical model of bacteria population under the antibiotic influence

Cited by 2 publications

References 10 publications

Inverse problems for a model of biofilm growth

Inverse problems for a model of biofilm growth

Teaching High School Students to Solve Differential Equations Using Python at Math Class

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