Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method. (29th November 2012)

• Record Type: Journal Article
• Authors: Hattaf, Khalid; Yousfi, Noura
• Other Names: Bahadur R. P. Academic Editor.; Panteleev M. A. Academic Editor.
• Is Part Of: ISRN biomathematics. Volume 2012(2012)
• Publication Date: 2012-11-29
• Subjects: Biomathematics -- Periodicals; Models, Biological; Biometry; Biomathematics; Electronic journals; Periodicals; Periodicals; Fulltext; Internet Resources; Periodicals; 570.151
• DOI: 10.5402/2012/215124
• Languages: English
• ISSNs: 2090-7702

Abstract

Abstract : We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4 + T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin's maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation.