of the Urals

Russian Journal of Agricultural Research

The publication is registered by the Ministry of the Russian Federation
for Affairs of the Press, Television and Radio Broadcasting and Mass Communication Media.
Registration certificate: PI number 77-12831 on May 31, 2002
Subscription index in catalog «Russian Press» - 16356
ISSN 1997 - 4868 (Print)

The Journal is included in the list of the leading peer-reviewed scientific journals and publications, which should be published by the main results of theses for the degree of doctor and Ph.D.
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Journal is included in the list of VAK (from 25.09.2017), No. 291

ISSN 2307-0005 (Online)
Key title: Agrarnyj vestnik Urala (Online)
Abbreviated key title: Agrar. vestn. Urala (Online)

Аграрный вестник Урала № 05 (172) 2018

Биология и биотехнологии

Ким А. В. доктор физико-математических наук, руководитель группы функционально-дифференциальных уравнений Институт математики и механики Уральского отделения Российской академии наук

Андрюшечкина Н. А. доцент, заведующая кафедрой, Уральский государственный аграрный университет

Новиков М. Ю. аспирант Институт математики и механики УрО РАН



The problem of constructing feedbackcontrol, stabilizing of the HIV model based on the theory of analytical designof regulators for systems with delay is considered in this article. The modelis described by a system of functional differential equations. A stabilizingcontrol is constructed basing on the method of explicit solutions ofGeneralized Riccati Equations of the theory of analytical constructingregulator for systems with delays. Currently, six variants of explicitsolutions to Generalized Equations of Riccati used for stabilization of systemswith aftereffect are identified. However, in the scientific literature,numerical modelling and stabilization of HIV models is discussed only by thefirst three methods. Numerical modelling of the stabilizing effect based on thefourth option explicit solutions to Generalized Equations of Riccati isconsidered in this article. A computer program for performing the necessarycalculations was developed


HIV-model, computational immunology, stabilization, differential equations with delay.


1. Balabayev T. F. Modeling and forecasting of HIV-infection: methodology and perspectives // Bulletin Of KazNMU. 2013. No. 4-1.

2. Bassey B. E., Lebedev K. A. On mathematical model of the impact of non-compliance with preventive measures for the prevention of the spread of HIV/AIDS among heterogeneous population. // Scientific Journal of KubSAU. 2015. No. 108.

3. Bolodurina I. P., Ivanova Yu. P. Optimum control of process of application of antivirus preparations at HIV infection threatment // Bulletin Of The SUSU. Ser. Computational mathematics and computer science. 2013. No. 4.

4. Kabanikhin S. I., Krivorotko O. I., Mortier A., Voronov D. A., Yermolenko D. V. A numerical algorithm of paremeter estimation for dynamic model for HIV infection of DC4+ T cells // The Siberian scientific medical journal. 2016. Vol. 36. No. 1.

5. Kwon V. H., Kim A. V., Kormyshev V. M., Pimenov V. G., Solodushkin S. I. Analytical design and synthesis of controllers for systems with aftereffect. Ekaterinburg : Publishing house of the Ural Federal University, 2010.

6. Kim A. V., Safronov M. A., Kormyshev V. M. Stabilization of the model of HIV infection in the human body // Agrarian Bulletin of the Urals. 2013. No. 11.

7. Karnaushenko Y. M., Tuzikov A. A., Kisel M. I., Andrianov A. V. Computer simulation Methods to develop new drugs against HIV-1 // Science and innovations. 2017. No. 167.

8. Ogban G. I., Lebedeb K. A. Mathematical model of the dynamics of HIV infection without threatment // Scientific Journal of KubSAU. 2015. No. 110.

9. Chereshnev V. A., Bocharov G. A., Kim A. V., Bazhan S. I., Gainova I. A., Krasovskii A. N., Shmagel N. G., Ivanov A.V., Safronov M. A., Tretyakov, R. M. Introduction to problems of modeling and controlling the dynamics of HIV infection. M.: Izhevsk : Institute of computer science, 2016. 236 p.

10. Chibilyaev V. A., Kulikov A. Yu., Yagudina R. I. Pharmacoeconomic modeling of antiretroviral drugs use during threatment of HIV infection // Pharmacoeconomics. Modern pharmacoeconomics and pharmacoepidemiology. 2013. No. 2.

11. Arts E. J., Hazuda D. J. HIV-1 Antiretroviral Drug Therapy. Cold Spring Harbor perspectives in medicine, 2(4) (2012), p. a007161.

12. Bocharov G., Chereshnev V., Gainova I., Bazhan S., Bachmetyev B., Argilaguet J., Martinez J., Meyerhans A. Human Immunodeciency Virus Infection: from Biological Observations to Mechanistic Mathematical Modelling. EDP Math. Model. Nat. Phenom. Vol. 7, No. 2, 2012. P. 1–29.

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