Agrarian
Bulletin
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

УДК:001.891.573

STABILIZATION OF THE HIV MODEL WITH DELAY BASED ON FOURTH VARIANT OF EXPLICIT SOLUTIONS OF GENERALIZED RICCATI EQUATIONS

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


Keywords:

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


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