Mathematical model for describing anti-virus immune response regulation allowing for functional disorders in a body
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.
- Voronin E.E., Latysheva I.B. VICh-infektsiya v Rossiiskoi Federatsii [HIV in the Russian Federation]. Ural'skii meditsinskii zhurnal, 2016, no. 9 (142), pp. 6–8 (in Russian).
- Zhdanov V.M., Bukrinskaya A.G. Reproduktsiya miksovirusov (virusov grippa i skhodnykh s nimi) [Mixoviruses reproduction (influenza viruses and those similar to them)]. Moscow, Meditsina, Publ., 1969, 280 p. (in Russian).
- Zaitseva N.V., Lanin D.V., Chereshnev V.A. Immunnaya i neiroendokrinnaya regulyatsiya v usloviyakh vozdeistviya khimicheskikh faktorov razlichnogo geneza [Immune and neuroendocrine regulation under exposure to chemical factors of various genesis]. Perm', Izdatel'stvo Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta, Publ., 2016, 236 p. (in Russian).
- Lanin D.V., Zaitseva N.V., Dolgikh O.V. Neiroendokrinnye mekhanizmy regulyatsii funktsii immunnoi sistemy [Neuroendocrine Mechanisms for Regulation of Immune System]. Uspekhi sovremennoi biologii, 2011, no. 2, pp. 122–134 (in Russian).
- Lanin D.V., Lebedeva T.M. Vozdeistvie khimicheskikh faktorov sredy obitaniya na funktsii i vzaimosvyazi regulyatornykh sistem u detei [The influence of chemical environmental factors on functions and interrelationships of regulatory systems in children]. Gigiena i sanitariya, 2016, vol. 95, no. 1, pp. 94–96 (in Russian).
- Marchuk G.I., Berbentsova E.P. Ostrye pnevmonii. Immunologiya, otsenka tyazhesti, klinika, lechenie [Acute pneumonias. Immunology, gravity assessment, clinical course, and treatment]. Moscow, Nauka,Publ., 1989, 304 p. (in Russian).
- Zaitseva N.V., Shur P.Z., May I.V., Kiryanov D.A. Metodicheskie podkhody k otsenke integral'nogo riska zdorov'yu naseleniya na osnove evolyutsionnykh matematicheskikh modelei [Approaches to the assessment of integrated health risk population based on evolution of mathematical models]. Zdorov'e naseleniya i sreda obitaniya, 2011, no. 10, pp. 6–9 (in Russian).
- Stepanenko L.A., Savchenkov M.F., Il'ina S.V., Anganova E.V., Savilov E.D. Otsenka sostoyaniya immu-nnoi sistemy detskogo naseleniya kak markera tekhnogennogo zagryazneniya okruzhayushchei sredy [An assessment of the immune status of the children population as a marker of technogenic pollution of the environment]. Gigiena i sanitariya, 2016, vol. 95, no.12, pp. 1129–1133 (in Russian).
- Poletaev A.B., Morozov S.G., Kovalev I.E. Regulyatornaya metasistema (immunoneiroendokrinnaya regulyatsiya gomeostaza) [Regulatory metasystem (immune-neuroendocrine homeostasis regulation)]. Moscow, Meditsina, Publ., 2002, 166 p. (in Russian).
- Savilov E.D., Il'ina S.V. Osobennosti infektsionnoi patologii detskogo naseleniya v usloviyakh tekhnogennogo zagryazneniya okruzhayushchei sredy [Features of Infectious Pathology in the Child Population in the Conditions of Technogenic Pollution of the Environment]. Epidemiologiya i vaktsinoprofilaktika, 2012, no. 1 (62), pp. 58–63 (in Russian).
- Savilov E.D., Mal'tsev M.V. Epidemiologicheskaya kharakteristika virusnogo gepatita S v usloviyakh krupnogo promyshlennogo goroda [Epidemiological characteristic of viral hepatitis с in large industrial city settings]. Zhurnal mikrobiologii, epidemiologii i immunobiologii, 2007, no. 1, pp. 70–71 (in Russian).
- Stepanenko L.A., Il'ina S.V., Savilov E.D. Osobennosti sostoyaniya spetsificheskogo immuniteta k upravlyaemym infektsiyam u detei (na primere kori i poliomielita) v usloviyakh vozdeistviya tekhnogennoi nagruzki [Peculiarities of specific immunity to manageable infections in children (on the examples of measles and polyomielitis) under impacts exerted by technogenic loads]. Byulleten' Vostochno-Sibirskogo nauchnogo tsentra Sibirskogo otdeleniya Rossiiskoi akademii meditsinskikh nauk, 2007, no. S3, pp. 66–68 (in Russian).
- Savilov E.D., Anganova E.V., Il'ina S.V., Stepanenko L.A. Tekhnogennoe zagryaznenie okruzhayushchei sredy i zdorov'e naseleniya: analiz situatsii i prognoz [Technogenic environmental pollution and the public health: analysis and prognosis]. Gigiena i sanitariya, 2016, vol. 95, no. 6, pp. 507–512 (in Russian).
- Zaitseva N.V., Kiryanov D.A., Lanin D.V., Chigvintsev V.M. A mathematical model of the immune and neuroendocrine systems mutual regulation under the technogenic chemical factors impact. Computational and Mathematical Methods in Medicine, 2014. Available at: https://www.hindawi.com/journals/cmmm/2014/492489/abs/ (18.04.2017)
- Andrew M.E., Churilla A.M., Malek T.R., Braciale V.L., Braciale T.J. Activation of virus specific CTL clones: antigen-dependent regulation of interleukin 2 receptor expression. J Immunol, 1985, no. 134 (2), pp. 920–925.
- Tamura S.I., Iwasaki T., Thompson A.H., Asanuma H., Chen Z., Suzuki Y., Aizawa C., Kurata T. Antibody-forming cells in the nasalassociated lymphoid tissue during primary influenza virus infection. Journal of General Virology, 1998, vol.79, no. 2, pp. 291–299.
- Ashley N.T., Demas G.E. Neuroendocrine-immune circuits, phenotypes, and interactions. Hormones and Behavior, 2017, vol. 87, pp. 25–34.
- Bairagi N., Chatterjee S., Chattopadhyay J. Variability in the secretion of corticotropin-releasing hor-mone, adrenocorticotropic hormone and cortisol and understandability of the hypothalamic-pituitary-adrenal axis dynamics – a mathematical study based on clinical evidence. Mathematical Medicine and Biology, 2008, vol. 25, no. 1, pp. 37–63.
- Bellavance M., Rivest S. The neuroendocrine control of the innate immune system in health and brain diseases. Immunological Reviews, 2012, vol. 248, no. 1, pp. 36–55.
- Bocharov G.A., Romanyukha A.A. Mathematical model of antiviral immune response III. Influenza A virus infection. Journal of Theoretical Biology, 1994, vol. 167, no. 4, pp. 323–360.
- Chapman C.R., Tuckett R.P., Song C.W. Pain and Stress in a Systems Perspective: Reciprocal Neural, Endocrine, and Immune Interactions. Journal of Pain, 2008, vol. 9, no. 2, pp. 122–145.
- Zabel P., Horst H.J., Kreiker C., Schlaak M. Circadian rhythm of interleukin-1 production of monocytes and the influence of endogenous and exogenous glucocorticoids in man. Klinische Wochenschrift, 1990, vol. 68, no. 24, pp. 1217–1221.
- Bergeron Y., Ouellet N., Deslauriers A., Simard M., Olivier M., Bergeron M. Cytokine kinetics and other host factors in response to pneumococcal pulmonary infection in mice. Infect. Immun, 1998, vol. 66, no. 3, pp. 912–922.
- Demas G.E., Adamo S.A., French S.S. Neuroendocrine-immune crosstalk in vertebrates and inverte-brates: Implications for host defence. Functional Ecology, 2011, vol. 25, no. 1, pp. 29–39.
- Pace T.W., Negi L.T., Adame D.D., Cole S.P., Sivilli T.I., Brown T.D., Issa M.J., Raison C.L. Effect of compassion meditation on neuroendocrine, innate immune and behavioral responses to psychosocial stress. Psy-choneuroendocrinology, 2009, no. 34, pp. 87–98.
- Felig P., Frohman L. Endocrinology and metabolism, 4er ed. New York, McGraw-Hill, Publ., 2001, 1562 p.
- Gloff C., Wills R. Pharmacokinetics and Metabolism of Therapeutic Cytokines. In B. Ferraiolo, M. Mohler, C. Gloff, eds. New York, Plenum Press, Publ., 1992, pp. 127–150.
- Haus E., Smolensky M.H. Biologic rhythms in the immune system. Chronobiology international, 1999, vol. 16, no. 5, pp. 581–622.
- Heffner K.L. Neuroendocrine Effects of Stress on Immunity in the Elderly: Implications for Inflamma-tory Disease. Immunology and Allergy Clinics of North America, 2011, vol. 31, no. 1, pp. 95–108.
- Heijnen C.J. Receptor regulation in neuroendocrine-immune communication: current knowledge and future perspectives. Brain, behavior, and immunity, 2007, vol. 21, no. 1, pp. 1–8.
- Julkunen I., Melen K., Nyqvist M., Pirhonen J., Sareneva T., Matikainen S. Inflammatory responses in influenza A virus infection. Vaccine, 2000, vol. 19, no. 1, pp. 32–37.
- Muraguchi A., Kehrl J.H., Longo D.L., Volkman D.J., Smith K.A., Fauci A.S. Interleukin 2 receptors on human B cells. Implications for the role of interleukin 2 in human B cell function. The Journal of experimental medicine, 1985, vol. 161, no. 1, pp. 181–97.
- Joklik W.K. Interferons. In: B.N. Fields, ed. New York, Raven Press, Publ., 1985, pp. 281–307.
- Keenan K.P., Combs J.W., McDowell E.M. Regeneration of hamster tracheal epithelium after mechanical injury. Virchows Archiv B Cell Pathology Including Molecular Pathology, 1983, vol. 42, no. 1, pp. 231–252.
- Kerdiles Y., Ugolini S., Vivier E. T cell regulation of natural killer cells. The Journal of Experimental Medicine, 2013, vol. 210, no. 6, pp. 1065–1068.
- Marchuk G.I., Petrov R.V., Romanyukha A.A., Bocharov G.A. Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B. Journal of Theoretical Biology, 1991, vol. 151, no. 1, pp. 1–40.
- Miyake S. Mind over cytokines: Crosstalk and regulation between the neuroendocrine and immune sys-tems. Clinical and Experimental Neuroimmunology, 2012, vol. 3, no. 1, pp. 1–15.
- Carroll B.J., Cassidy F., Naftolowitz D., Tatham N.E., Wilson W.H., Iranmanesh A., Liu P.Y., Veldhuis J.D. Pathophysiology of hypercortisolism in depression. Acta Psychiatrica Scandinavica, 2007, vol. 115, pp. 90–103.
- Ronni T., Sareneva T., Pirhonen J., Julkunen I. Activation of IFN-alpha, IFN-gamma, MxA, and IFN regulatory factor 1 genes in influenza A virus-infected human peripheral blood mononuclear cells. Journal of im-munology, 1995, vol. 154, no. 6, pp. 2764–2774.
- Sareneva T., Matikainen S., Kurimoto M., Julkunen I. Influenza A virus-induced IFN-alpha/beta and IL-18 synergistically enhance IFN-gamma gene expression in human T cells. Journal of immunology, 1998, vol. 160, no. 12, pp. 6032–6038.
- Suarez E.C., Sundy J.S., Erkanli A. Depressogenic vulnerability and gender-specific patterns of neuro-immune dysregulation: What the ratio of cortisol to Creactive protein can tell us about loss of normal regulatory control. Brain, Behavior, and Immunity, 2015, no. 44, pp. 137–147.
- Vinther F., Andersen M., Ottesen J.T. The minimal model of the hypothalamic-pituitary-adrenal axis. Journal of Mathematical Biology, 2011, vol. 63, no. 4, pp. 663–690.
- Wohlfartt C. Neutralization of Adenoviruses: Kinetics, Stoichiometry, and Mechanisms. J Immunol, 1988, vol. 62, no. 7, pp. 2321–2328.
- World Health Organization World Health Organization. World health statistics 2016: monitoring health for the SDGs, sustainable development goals. World Health Organization, 2016, 121 p.