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 № 11 (117) 2013

Биология и биотехнологии

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

Кормышев В. М. кандидат технических наук, доцент, заведующий кафедрой Уральский федеральный университет имени первого Президента России Б. Н. Ельцина

Сафронов М. А. аспирант Уральский федеральный университет имени первого Президента России Б. Н. Ельцина

УДК:001.891.573

Modeling and stabilization of distribution HIV infection in the human body

 Considers a problem of stabilizing a mathematical model of HIV dynamics is considered. The problem of construction
of feedback control, which stabilizes the HIV model. The mathematical model described by a system of linear functional
differential equations, which allows you to apply for building construction management, the theory of analytical design
of controllers for systems with delays. The model is described by a system of functional differential equations. A stabilizing
control is constructed basing on the method of explicit solutions of Generalized Riccati’s Equations of the theory of analytical
constructing regulator for systems with delays. For construct a feedback control we use the variant of explicit solutions
of the generalized Riccati’s equations (the study of control stabilizing properties based on other variants discussed in previous
authors articles). Stabilizing control for the system of differential equations with delay supports HIV-infection model spread at
a certain sufficiently small non-zero level. Results of the research can be applied to analysis of some aspects of HIV dynamics.


Keywords:

modeling, HIV, differential equations with delay, Riccati’s generalized equations


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