Authors:
A. V. KIM, doctor of physics and mathematics sciences, professor,
N. A. ANDRJUSHECHKINA, associate professor, head of the department,
M. Yu. NOVIKOV, postgraduate student,
Russian Academy of Science, Ural branch, Institute of Mathematics and Mechanics (16 S. Kovalevskaya str., 620990, Ekaterinburg; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.),
Ural State Agrarian University (42 K. Liebknecht str, 620075, Ekaterinburg; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.),
Abstract. The problem of constructing feedback control, stabilizing of the HIV model based on the theory of analytical design of regulators for systems with delay is considered in this article. 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 Equations of the theory of analytical constructing regulator for systems with delays. Currently, six variants of explicit solutions to Generalized Equations of Riccati used for stabilization of systems with aftereffect are identified. However, in the scientific literature, numerical modelling and stabilization of HIV models is discussed only by the first three methods. Numerical modelling of the stabilizing effect based on the fourth option explicit solutions to Generalized Equations of Riccati is considered in this article. A computer programm for performing the necessary calculations was developed. The obtained data can be used in further research related to the design control based on the fifth and sixth variants of the solution of the Generalized Riccati Equations, as well as for the analysis HIV dynamics at different initial parameters.
Keywords: HIV-model, computational immunology, stabilization, differential equations with delay.
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