A system theoretic study on a treatment of AIDS patient by achieving long-term non-progressor

Abstract

There has been much recent interest in the long-term non-progressor (LTNP), who has been infected with human immunodeficiency virus (HIV) but does not proceed to AIDS. Under the assumption that a mathematical model describing the HIV infection and drug effects is true for real systems, we claim that it is possible to steer the state of any patients to that of LTNP if the model parameters belong to the proposed parameter intervals. Once the state is transferred close to LTNP, CTL memory is established and the viral load remains very low level even after the medication is stopped. In order to justify the claim, we first analyze the stability and the bifurcation of the model and show that there exists an equilibria curve towards LTNP, which is stable for all fixed constant inputs except some singular points. Then, we propose a new treatment strategy based on a useful property of Non-vanishing Basin of Attraction (NvBA)-stability. An extensive simulation study is also included to validate the proposed treatment for various initial conditions and to show the robustness against the parameter uncertainty. From a practical perspective, it deserves further investigation whether the proposed treatment strategy could switch a patient into LTNP in the real world. (C) 2008 Elsevier Ltd. All rights reserved.