Optimal control of an HIV infection model with the adaptive immune response and two saturated rates.

The dynamics of a model describing the human immunodeficiency virus (HIV) infection with cytotoxic T-lymphocyte (CTL), antibodies and two saturated rates is investigated and studied in this paper. The model includes five nonlinear differential equations describing the evolution of uninfected cells, infected ones, free HIV viruses, CTL immune response and antibodies. This model includes also two treatments that represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence, positivity and boundedness of solutions are given. Existence of the optimal control pair is established and the Pontryagin's maximum principle is used to find an optimal treatment strategy that maximizes the number of uninfected CD4⁺ T cells as well as cytotoxic T-lymphocyte and antibody immune responses. Finally, the optimality system is derived and solved numerically. Results show that administrating good therapy maximizes the amount of healthy CD4⁺ T cells and deceases considerably the viral load and the infected cells. [ABSTRACT FROM AUTHOR]