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.
The Journal is included in the Russian Science Citation Index.
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


Results of stabilization of the spread of HIV infection in the human body

 Results of research stabilizability of the mathematical model describing HIV dynamics are given. 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). Management features tend to some nonzero value
controls support the replication of HIV in the body in a certain steady-state. The third version control stabilizes the spread of
HIV infection in humans is approximately 2 times faster than the first version control. In the case of the third embodiment of
the control in the human body is more T-cells, and the percentage of infected T-cells are less of free viral cells also remains
more. The amount of free viral cells may be reduced by the addition of external influences, for example, administration of an
antiviral drug. 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.


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


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