Abstract
We study the stability and feedback stabilization of the uninfected steady state of a human immunodeficiency virus (HIV) infection model. The model is a 6‐dimensional nonlinear ODEs that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages, and takes into account the Cytotoxic T Lymphocytes (CTLs) immune response. Lyapunov function is constructed to establish the global asymptotic stability of the uninfected steady state of the model. In a control system framework, the HIV infection model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is considered as a nonlinear control system with drug dose as control input. We developed treatment schedules for HIV‐infected patients by using Model Predictive Control (MPC‐)based method. The MPC is constructed on the basis of an approximate discrete‐time model of the HIV infection model. The MPC is applied to the stabilization of the uninfected steady state of the HIV infection model. Besides model inaccuracies that HIV infection model suffers from, some disturbances/uncertainties from different sources may arise in the modelling. In this work the disturbances are modelled in the HIV infection model as additive bounded disturbances. The robustness of the MPC against small model uncertainties or disturbances is also shown.
Highlights
In the last decade many mathematical models have been proposed to describe the immunological response to infection with the human immunodeficiency virus HIV
Some of these models mainly represent the interaction of the HIV with the CD4 T cells, others take into account the Cytotoxic T Lymphocytes CTLs immune response 1
The first purpose of the present paper is to study the basic properties of an HIV infection model which describes the interaction of the HIV with two target cells, CD4 T cells and macrophages and takes into consideration the CTL immune response
Summary
HIV is responsible of acquired immunodeficiency syndrome AIDS Some of these models mainly represent the interaction of the HIV with the CD4 T cells, others take into account the Cytotoxic T Lymphocytes CTLs immune response 1. Perleson et al, observed that after the rapid first phase of decay during the initial 1-2 weeks of antiretroviral treatment, plasma virus levels declined at a considerably slower rate 15 This second phase of viral decay was attributed to the turnover of a longer-lived virus reservoir of infected cells. The first purpose of the present paper is to study the basic properties of an HIV infection model which describes the interaction of the HIV with two target cells, CD4 T cells and macrophages and takes into consideration the CTL immune response. The global stability of the uninfected steady state of the model is established using a Lyapunov approach
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