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

Anastasia I. Lavrova (), Dilyara S. Esmedljaeva and Eugene B. Postnikov ()
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Anastasia I. Lavrova: Sophya Kovalevskaya North-West Mathematical Research Center, Immanuel Kant Baltic Federal University, Nevskogo St. 14, 236041 Kaliningrad, Russia
Dilyara S. Esmedljaeva: Saint-Petersburg State Research Institute of Phthisiopulmonology, Ligovskiy Prospect 2-4, 194064 Saint Petersburg, Russia
Eugene B. Postnikov: Theoretical Physics Department, Kursk State University, Radishcheva St. 33, 305000 Kursk, Russia

Mathematics, 2023, vol. 11, issue 21, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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