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JOURNALS // Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika // Archive

Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2025 Number 93, Pages 5–18 (Mi vtgu1132)

MATHEMATICS

Experimental study and identification of kinetic parameters of the process of bacterial inactivation in the presence of iodine vapor

A. B. Vorozhtsov, I. S. Bondarchuk, A. O. Prokopchuk, E. S. Marchenko, S. D. Sokolov

Tomsk State University, Tomsk, Russian Federation

Abstract: The article presents results of an experimental study of the inactivation process of the model bacterial strain L. casei ATCC 393 in the presence of iodine vapor at temperatures of $T = 27, 37, 40$ and $42^{\circ}$C.; kinetic curves of survival under the influence of iodine vapor at the given temperatures have been obtained. The results of the experimental study demonstrate the high efficiency of iodine vapor against the model bacterial strain. A nonlinear Weibull model is proposed to describe the inactivation process of the model bacterial strain L. casei ATCC 393 under the influence of iodine vapor at different temperatures ($T = 27, 37, 40$, and $42^{\circ}$C). The problem of identifying the model parameters is set as an optimization problem in order to minimize the spread of one of the determined parameters. The identification process includes a sequential solution of the inverse and direct kinetic problems and subsequent comparison of the calculated values with the experimental data, which confirms the adequacy of the model. Microsoft Excel software is used for the kinetic analysis and evaluation of the model parameters. The criterion for selecting the optimal parameters of the mathematical model of the process is the minimum value of the statistical functional in the form of the variation coefficient and the maximum value of the nonlinear determination coefficient $R^2$. High values of the determination coefficient $R^2$ from $0.94$ to $0.99$ confirm the adequacy of the model. It is shown that the Weibull model is suitable for the qualitative and quantitative analysis of the inactivation process of the model bacterial strain L. casei ATCC 393 under the influence of iodine vapor at different temperatures $T = 27, 37, 40$, and $42^{\circ}$C).

Keywords: biokinetics, mathematical model, kinetic parameters, Weibull model, determination coefficient $R^2$.

UDC: 51-76

MSC: 92-08, 92-10

Received: 02.12.2024
Accepted: February 7, 2025

DOI: 10.17223/19988621/93/1



© Steklov Math. Inst. of RAS, 2026