Mathematical model for describing anti-virus immune response regulation allowing for functional disorders in a body

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P.V. Trusov1, 2, N.V. Zaitseva1, V.M. Chigvintsev1, 2, D.V. Lanin1, 3


1Federal Scientific Center for Medical and Preventive Health Risk Management Technologies, 82 Monastyrskaya Str., Perm, 614045, Russian Federation
2Perm National Research Polytechnic University, 29 Komsomolskiy avenue, Perm, 614990, Russian Federation
3Perm State University, 15 Bukireva Str., Perm, 614990, Russian Federation


Our task was to create a mathematical model which could describe anti-virus immune response regulation allowing for disorders in the adaptation (neuroendocrine and immune) systems caused by chemical factors of various genesis. We analyzed immune response allowing for immunity types (inborn and acquired one) with certain quantitative parameters chosen in order to characterize them, notably: interferon and NK-cells for inborn immunity, and virus-specific cytotoxic T-cells and antibodies-forming B-lymphocytes for acquired immunity. Regulatory mechanisms incorporated in the model comprise influences exerted by hypothalamus-hypophysis-adrenals system hormones (corticoliberin, adrenocorticotropic hormone, and hydrocortisone), and cytokines (interleukin-1 and interleukin-2) produced by various regulatory cells of the immune system. The suggested model also takes spatial organization of infection and immune processes in different organs and tissues into account as we introduced a time lag for components interaction into it.

The model includes a system of 18 ordinary differential equations with a retarded argument; its parameters characterize how fast various processes influencing an infection dynamics evolve in a body. The parameters are identified on the basis of published experimental data which describe a process of a body being infected with a virus. We calculated dynamics in the immune and neuroendocrine system parameters under a virus infection allowing for disorders in the marrow synthetic function. The model is developed within the framework of a concept viewing a human body as a multi-level model allowing for interactions between its systems and functional state of examined organs under influences exerted on them by hazardous factors of different genesis. The performed research gives a qualitative idea on biological factors which explain an infectious agent kinetics under a virus infection and impacts exerted by factors of various genesis. The results can be applied for adjusting parameters of existing population models, spread and clinical course of various infections, and for making long-term forecasts on an epidemiologic situation which is necessary when we analyze infectious diseases risks, including those which occur under impacts exerted on a human body by hazardous environmental factors.

mathematical model, dynamic system, virus disease, inborn immunity, acquired immunity, neuroendocrine regulation
Trusov P.V., Zaitseva N.V., Chigvintsev V.M., Lanin D.V. Mathematical model for describing antivirus immune response regulation allowing for functional disorders in a body. Health Risk Analysis, 2017, no. 4, pp. 117–128. DOI: 10.21668/health.risk/2017.4.13.eng
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