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Home Archive 2020 № 3 INTEGRATED MATHEMATICAL MODEL FOR IMITATION OF THE COURSE OF VIRAL DISEASE AND CORRECTION OF THE INDUCED HYPOXIC STATE N. I. Aralova, O. M. Klyuchko, V. I. Mashkin , I. V. Mashkina, T. A. Semchyk
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ISSN 2410-7751 (Print)
ISSN 2410-776X (Online)

Biotechnologia Acta V. 13, No 3, 2020
Р. 30-44, Bibliography 138, English
Universal Decimal Classification: 519.8.612.007
https://doi.org/10.15407/biotech13.03.030

INTEGRATED MATHEMATICAL MODEL FOR IMITATION OF THE COURSE OF VIRAL DISEASE AND CORRECTION OF THE INDUCED HYPOXIC STATE

N. I. Aralova1, O. M. Klyuchko 2, V. I. Mashkin 1 , I. V. Mashkina 1, T. A. Semchyk1

1 Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv
2 National Aviation University, Kyiv, Ukraine

The aim of the work was to create a complex mathematical model simulating the course of the disease caused by the SARS-CoV-2 virus on the level of interaction between functional systems of organism and pharmacological correction of organism hypoxic states arising in the complicated course of the disease. In the present work the methods of mathematical modeling and theory of optimal control of moving objects were used. The proposed integrated mathematical model consisted on the mathematical models of functional systems of respiration and blood circulation, thermoregulation, immune response, erythropoesis, and pharmacological correction. Individual patient data were taken for this model, and the disturbing effect in the form of viral disease was simulated. The reactions of functional respiratory and blood circulatory systems were predicted. Partial pressures of respiratory gases in alveolar spaces and their tensions in lung capillaries blood, arterial and mixed venous blood, and tissue fluid were calculated. Further the intravenous injection of antihypoxant was simulated and the values of the same parameters were calculated. In such a way it was possible to choose the most optimal way of hypoxic state correction for any individual. This model is theoretical only for today because the models of respiratory and blood circulation systems were designed for the average person and it does not suppose peculiarities of individual persons infected with SARS-CoV-2. In particular, this concerns the peculiarities of gas exchange in the alveolar space and characteristics of respiratory gases diffusion through the alveolar-capillary and capillary-tissue membranes. However, it is one of possible directions for solving the complex tasks related to treatment of the disease caused by SARS-CoV-2 virus. In the result of the work the complex of information support for the imitation of viral disease course was developed at the level of interaction of organism functional systems, as well as pharmacological correction of caused by it hypoxic states.

Key words: SARS-Cov-2 virus, immune response model, mathematical model of the respiratory system, hypoxic state, infection lesion

© Palladin Institute of Biochemistry of National Academy of Sciences of Ukraine, 2020

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      101. Onopchuk Yu. N., Aralova N. I., Beloshitsky P. V., Klyuchko O. M. Integral estimation of human reliability and work ability during wrestling. Bulletin of Engineering Academy of Ukraine. 2015, N 3, P. 145‒148 (In Russian).

      102. Aralova N. I., Onopchuk Yu. N. Dynamics of voluremetric velocity of blood flow at physical loading of trained persons. Analysis of computational experiments with mathematical model. Cybernetics. 1990, N 3, P. 125‒127 (In Russian).

      103. Onopchuk Yu. N., Aralova N. I., Beloshitsky P. V., Podlivaev B. A., Mastucash Yu. I. Forecasting of wrestler’ state in the combat on the base of mathematic model of functional respiratory system. Computer mathematics. 2005, N 2, P. 69‒79 (In Russian).

      104. Aralova A. A., Aralova N. I., Kovalchuk-Khimyuk L. A., Onopchuk Yu. N. Automated information system for athletes functional diagnostics. Control systems and machines. 2008, V. 3, P. 73–78 (In Russian).

      105. Beloshitsky P. V., Onopchuk Yu. N., Aralova N. I., Podlivaev B. A. Mathematic forecasting of wrestler’ state during combat. Sport medicine. 2009, N 1‒2, P. 55‒59 (In Ukrainian).

      106. Aralova N. I., Onopchuk Yu. N., Podlivaev B. A. Mathematic models for control of sportive combat. International Workshop “Prediction and Decision Making under Uncertainties (PDMU-2004), Abstracts. Ternopil, Ukraine. 2004 (In Ukrainian).

      107. Aralova N. I. Information technologies of decision making support for rehabilitation of sportsmen engaged in combat sport. Journal of Automation and Information Sciences. 2016, V. 3, P. 160–170.

      108. Aralova A. A., Aralova N. I., Beloshitsky P. V., Onopchuk Yu. N. Automated Information System for Functional Diagnostics of Mountaineers. Sports Medicine. 2008, V. 1, P. 163‒169.

      109. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N. Results of investigations of adaptation problems by Ukrainian scientists in Prielbrussie. Bulletin of NAU. 2008, V. 1, P. 102‒108 (In Ukrainian).

      110. Onopchuk Yu. N., Beloshitsky P. V., Klyuchko O. M. Creation of mathematic models on the results of investigations of Ukrainian scientists at Elbrus. Bulletin of NAU. 2008, V. 3, P. 146‒155 (In Ukrainian).

      111. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N., Kolchinskaya A. Z. Results of investigations of high nervous activity by Ukrainian scientists in Prielbrussie. Bulletin of NAU. 2009, V. 2, P. 105‒112 (In Ukrainian).

      112. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N. Results of some medical and biological investigations of Ukrainian scientists at Elbrus. Bulletin of NAU. 2007, V. 3, P. 10‒16 (In Ukrainian).

      113. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N. Studying of hypoxia problem by Ukrainian scientists at Elbrus region. Bulletin of NAU. 2007, V. 2, P. 44‒50 (In Ukrainian).

      114. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N. Results of investigations by Ukrainian scientists of mountain factors influense on the health and life duration in Prielbrussie. Bulletin of NAU. 2008, V. 4, P. 102‒108 (In Ukrainian).

      115. Beloshitsky P. V., Klyuchko O. M., Onopchuk Yu. N. Results of investigations of structural and functional inter-relations by Ukrainian scientists in Prielbrussie. Bulletin of NAU. 2009, V. 1, P. 61‒67 (In Ukrainian).

      116. Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Mathematical models and integral estimation of organism systems reliability in extreme conditions. Electronics and control systems. 2016, V. 1, P. 107‒115. https://doi.org/10.18372/1990-5548.47.10295

      117. Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Investigation of reliability of operators work at fluctuating temperature conditions. Electronics and control systems. 2016, V. 2, P. 133‒140. https://doi.org/10.18372/1990-5548.48.11227

      118. Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Mathematical model for research of organism restoring for operators of continuously interacted system. Electronics and control systems. 2016, V. 3, P. 100‒105. https://doi.org/10.18372/1990-5548.49.11245

      119. Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Technical complex for selection, current medical control and rehabilitation of flight personnel members. Mater. Sci.-Tech. Conference «Problems of development of global system for connections, navigation, monitoring and air flights organization CNS/ATM». November 2123, 2016. Kyiv: NAU. 2016, P. 114 (In Ukrainian).

      120. Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Mathematic modeling of functional self-organization of pilots’ respiration. «Integrated intellectual robototechnical complexes». «IIRTC-2017»: ХІ Conf. Mater. Kyiv: «NAU-druk». 2018, P. 268‒269 (In Ukrainian).

      121. Aralova А. А., Aralova N. I., Klyuchko O. M., Mashkin V. I., Mashkina I. V. Information system for the examination of organism adaptation characteristics of flight crews’ personnel. Electronics and control systems. 2018, V. 2, P. 106‒113. https://doi.org/10.18372/1990-5548.56.12944

      122. Aralova А. А., Aralova N. I. Authomatized information system for the estimation of functional respiratory system. Physiol. J. 2008, 54 (4), P. 57 (In Russian).

      123. Klyuchko O. M., Aralova N. I., Aralova A. A.Electronic automated work places for biological investigations Biotechnol. acta. 2019, 12 (2), 5‒26. https://doi.org/10.15407 /biotech12/02/005

      124. Aralova N. I. Evaluation of respiratory functional system, oxygen regimes of human organisms and the degree of hypoxia (a set of programs for PC). Physiol. J. 1996, 42 (3–4), 96 (In Russian).

      125. Aralova N. I., Mashkin V. I. The equations of inert gases dynamics for optimization of decision-making in providing safe decompression of the aquanaut. Theory of optimal solutions. 2018, V. 17, P. 62‒68.

      126. Aralova N. I., Mashkin V. I., Mashkina I. V. Information technologies for decisionmaking support for providing of aquanauts decompression security in conditions of hyperbaric hypoxia. Mater. of 6-th Intern. Conferense “Mathematic modeling, optimization and information technologies”, Kishiney, Moldova Republic, November 12–16, 2018. Kishiney: Evrika. 2018, P. 248–251 (In Russian).

      127. Beloshitskiy P. V., Onopchuk Yu. N., Aralova N. I. Mathematical models of respiratory systems and circulation of the blood systems as well as the estimation of organism’s reserves and of the reliability of system’s function. Eur. J. Physiol. 1995, Supp. to 430 (4). (Abstracts of the of the First FEPS Congress 9‒12 Sept., 1995, Maastricht, The Netherland). https://doi.org/10.1007/BF00591375

      128. Aralova N. I., Mastykash Yu. I., Mashkina I. V. Information technologies for the studying of work ability reserves of human organism during the work in extreme high mountain conditions. Mater.Conf. «Information problems of computer systems, jurisprudence, energetics, economy, modeling and management Step to the Science. Collection of research works of Buchach Institute of Management. Buchach. 2011, V. 7, P. 195‒198 (In Ukrainian).

      129. Aralova N. I., Mashkina I. V. Studying at mathematic models of organism adaptation possibilities for changed environmental conditions. Combinatory optimization and fuzzy multitudes: (Конем-2013). Mater. of III All-Ukrainian Sci. Seminar (Poltava, August 3031, 2013). Ed. Dr. Sci., Prof. O. O. Emetz. Poltava: PUET. 2013, P. 5‒7 (In Russian).

      130. Aralova N. I. Mathematical models of estimation of depletion of functional systems of human body after exposure to hypoxia hypermetabolic and effectiveness correction. X Intern. Sci.-Pract. Conference «Domestic Science in Epoque of Changes: Postulates of the Past and Theories of New Time», part 7. 2015, V. 10, P. 7‒11 (In Russian).

      131. Aralova N. I., Beloshitsky P. V., Klyuchko O. M. Mathematical models of system mechanisms of organism adaptation to hypoxia Abstracts 7th Chronic Hypoxia Symposium Feb 23Mar 2, 2019. La Paz. Bolivia Dedicated to the Late Danish Prof. Poul Erik Paulev. P. 24.

      https://zuniv.net/symposium7/Abstracts7CHS.pdf

      132. Marchenko D. I., Byts A. V., Semchik T. A. A multicriterial problem of system blood stream distribution in organs and tissues and an algorithm to its solution. Cybernetics and system analysis. 2001, V. 5, P. 132‒141.

      133. Aralova N. I. Mathematical models of decision support by the training in extreme conditions. IX Intern. Sci.-Pract. Conference «Domestic Science in Epoque of Changes: Postulates of the Past and Theories of New Time», part 7. 2015, V. 9, P. 7‒9.

      134. Aralova N. I. Information means for optimizing the process of athlete body recovery. Sports Medicine and physical rehabilitation. 2017, V. 1, P. 88‒96.

      135. Marchuk G. I., Pogozhev I. B., Zuev S. M. Similarity conditions in systems of interacting particles. Doc. RAS. 1995, 345 (5), 605‒606.

      136. Belykh L. N. Analysis of some mathematical models in immunology. Moskva: OVM AN USSR. 1984, 147 p.

      137. 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. J. Theor. Biol. 1991, 151 (1), 1–40. https://doi.org/10.1016/S0022-5193(05)80142-0

      138. Liashko N. I., Onopchuck G. Yu. Pharmacological correction of organism state. Mathematical model and its analysis. Computer Mathematics. 2005, V. 1, P. 127–134. (In Russian).



 

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Home Archive 2020 № 3 INTEGRATED MATHEMATICAL MODEL FOR IMITATION OF THE COURSE OF VIRAL DISEASE AND CORRECTION OF THE INDUCED HYPOXIC STATE N. I. Aralova, O. M. Klyuchko, V. I. Mashkin , I. V. Mashkina, T. A. Semchyk

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