Аграрный вестник Урала № 11 (117) 2013

Биология и биотехнологии

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.

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Keywords:

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

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