Rad HAZU, Matematičke znanosti, Vol. 24 (2020), 131-148.

CONTROL DESIGN OF AN HIV-1 MODEL

Amel Rahmoun, Djamila Benmerzouk and Bedr'Eddine Ainseba

Bordeaux Mathematics Institute, UMR CNRS 52 51, Case 36, Université Victor Segalen Bordeaux 2, 3 ter place de la Victoire, F 33076 Bordeaux Cedex, France
e-mail: Bedreddine.ainseba@u-bordeaux.fr

Abstract.   In this paper, we formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV), combined with nonlinear continuous feedback control. The detailed computations of two linearizing inputs is presented. It results in the design of a first fully linearizable system and a second partially linearizable one. The proposed controllers have the ability to drive the system close to the healthy equilibrium state. Numerical simulations demonstrate them effectiveness by maintaining virus concentration in very low levels and healthy cells in satisfactory levels.

2020 Mathematics Subject Classification.   92B99, 93C10, 93D15, 16W25, 37M05.

Key words and phrases.   Mathematical biology, nonlinear systems, stabilization of systems by feedback, Lie derivatives, simulations.

DOI: https://doi.org/10.21857/yk3jwhx3j9

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