HIV dynamics: Analysis and robust multirate MPC-based treatment schedules

Document Type : Original Article

Authors

Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa.

Abstract

Abstract:
Analysis and control of human immunodeficiency virus (HIV) infection have attracted
the interests of mathematicians and control engineers during the recent years. In this
paper we study the basic properties of a 6-dimensional HIV model that describes the
interaction of HIV with two target cells, CD4+ T cells and macrophages. Besides model
inaccuracies that HIV models suffer from, some disturbances/uncertainties from
different sources may arise in the modelling. The disturbances are modelled in the HIV
model as additive bounded disturbances. Highly Active AntiRetroviral Therapy
(HAART) is used. The control input is defined to be dependent on the drug dose and
drug efficiency. We developed a treatment schedules for HIV infected patients by using
robust multirate Model Predictive Control (MPC)-based method. The MPC is
constructed on the basis of the approximate discrete-time model of the nominal model.
We established a set of conditions, which guarantee that the multirate MPC practically
stabilizes the exact discrete-time model with disturbances. The proposed method is
applied to the stabilization of the uninfected steady state of the HIV model. The results
of simulations show that, after initiation of HAART with a strong dosage, the viral load
drop quickly and it can be kept under a suitable level with mild dosage of HAART.
Moreover, the immune system is recovered with some fluctuations due to the presence
of disturbances.

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