HIV-infection model stabilization

Abstract

In the paper considers a problem of stabilizing the system of differential equations with delay that described HIV infection dynamics mathematical model. 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 of functional differential equations. For construct a feedback control we use the second variant of explicit solutions of the generalized Riccati equations. First and third variants of stabilization discussed in other authors articles. To determine the parameters of the stabilization control based on the second variant of explicit solutions of generalized Riccati equation should be found special exponential matrix equation solution. Considered stabilizing control for the system of differential equations with delay leads HIV-infection system to the small non-zero level of infection. Results of the research can be applied to analysis of some aspects of HIV dynamics. © 2015, IFAC Hosting by Elsevier Ltd.