Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis

Lavrova, Anastasia I.; Esmedljaeva, Dilyara S.; Postnikov, Eugene B.

doi:10.3390/math11214522

Open AccessArticle

Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis

by

Anastasia I. Lavrova

^1,2,*

,

Dilyara S. Esmedljaeva

²

and

Eugene B. Postnikov

^3,*

¹

Sophya Kovalevskaya North-West Mathematical Research Center, Immanuel Kant Baltic Federal University, Nevskogo St. 14, 236041 Kaliningrad, Russia

²

Saint-Petersburg State Research Institute of Phthisiopulmonology, Ligovskiy Prospect 2-4, 194064 Saint Petersburg, Russia

³

Theoretical Physics Department, Kursk State University, Radishcheva St. 33, 305000 Kursk, Russia

^*

Authors to whom correspondence should be addressed.

Mathematics 2023, 11(21), 4522; https://doi.org/10.3390/math11214522

Submission received: 15 October 2023 / Revised: 29 October 2023 / Accepted: 30 October 2023 / Published: 2 November 2023

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)

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Abstract

Tuberculosis (TB) has a long history as a serious disease induced by its causative agent Mycobacterium tuberculosis. This pathogen manipulates the host’s immune response, thereby stimulating inflammatory processes, which leads to an even greater imbalance of specific enzymes/inhibitors that contribute to tissue destruction. This work addresses a model consisting of two ordinary differential equations obtained by reducing a previously developed large-scale model describing lung damage, taking into account key metabolic pathways controlled by bacteria. The resulting system is explored as a dynamical system simulating the interaction between bio-markers (matrix metalloproteinases) of tissue destruction and the pathogen. In addition to the analysis of the mathematical model’s features, we qualitatively compared the model dynamics with real clinical data and discussed their mutual correspondence.

Keywords: host–pathogen model; M. tuberculosis; nonlinear ODE; mathematical biophysics

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MDPI and ACS Style

Lavrova, A.I.; Esmedljaeva, D.S.; Postnikov, E.B. Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis. Mathematics 2023, 11, 4522. https://doi.org/10.3390/math11214522

AMA Style

Lavrova AI, Esmedljaeva DS, Postnikov EB. Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis. Mathematics. 2023; 11(21):4522. https://doi.org/10.3390/math11214522

Chicago/Turabian Style

Lavrova, Anastasia I., Dilyara S. Esmedljaeva, and Eugene B. Postnikov. 2023. "Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis" Mathematics 11, no. 21: 4522. https://doi.org/10.3390/math11214522

APA Style

Lavrova, A. I., Esmedljaeva, D. S., & Postnikov, E. B. (2023). Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis. Mathematics, 11(21), 4522. https://doi.org/10.3390/math11214522

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis

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