# Numeric modeling of bacteria population evolution in human lungs

N.E. Pil^{1}, V.M. Chigvintsev^{2}

^{1}Perm National Research Polytechnic University, 29 Komsomolskiy Ave., Perm, 614990, Russian Federation

^{2}Federal Scientific Center for Medical and Preventive Health Risk Management Technologies, 82 Monastyrskaya Str., Perm, 614045, Russian Federation

The present work focuses on building up a mathematical model showing bacteria population evolution in human lungs taking into account dynamics of immune processes; the model would be useful for assessing functional damage to the lungs. Numeric modeling of processes that occur in a human body is a promising tool for analyzing and predicting impacts exerted by risk factors on health. The suggested approach was developed within a concept describing a human body as a multi-level model that allowed for interaction between various systems and functional state of examined organs given effects produced on them by different adverse factors. Since direct modeling of the structure and processes occurring in the lungs is rather complicated, these organs are usually described with a porous medium model and it requires a lot of computing resources. Damage to the lungs determined via an evolution equation was introduced into the model. The equation described dependence between damage and infiltrate distribution and effects produced on alveolar cells by toxicants excreted by bacteria.

The work dwells on certain results that characterize how concentrations of immune system components and bacteria population are spatially distributed when an immune response is evolving. Our research provides a qualitative insight into reasons for quantitative changes in bacteria population under immune reactions occurring in a body under exposure to different factors. This approach can be used for obtaining more precise parameters for existing population models that show spread and clinical course of bacterial infections and for making a long-term prediction of an epidemiological situation. Results obtained with this approach can be useful for analyzing risks of communicable diseases including those occurring under exposure to adverse environmental factors.

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