title: Optimal control therapy and vaccination for special HIV-1 model with delay.
abstract: In this paper, we consider a four dimensional model of the human immunodeficiency virus-1 (HIV-1) with delay, which is an extension of some three dimensional models. We approach the treatment problem by adding two controllers to the system for inhibiting viral production. The optimal controller [Formula: see text] is considered for vaccine and [Formula: see text] for the drug. The Pontryagin maximum principle with delay is used to characterize these optimal controls. At the end, numerical results are presented to illustrate the optimal solutions. The validity of the model was confirmed by proper semi-quantitative simulation of some clinical data. The model was used to predict the possible beneficial effects of vaccine and anti-retroviral drug administration in HIV-1 disease.
authors.affiliation: Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad (FUM), Mashhad, Iran.
authors.forename: Elham
authors.initials: E
authors.lastname: Shamsara
authors.affiliation: Pharmaceutical Research Center, School of Pharmacy, Mashhad University of Medical Sciences, Mashhad, Iran.
authors.forename: Jamal
authors.initials: J
authors.lastname: Shamsara
authors.affiliation: Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad (FUM), Mashhad, Iran. afsharnezhad@math.um.ac.ir.
authors.forename: Zahra
authors.initials: Z
authors.lastname: Afsharnezhad
mesh_terms: D000465:Algorithms; D015496:CD4-Positive T-Lymphocytes / Q000821:virology; D003198:Computer Simulation; D015658:HIV Infections / Q000517:prevention & control* / Q000628:therapy; D015497:HIV-1 / Q000472:pathogenicity*; D006801:Humans; D008962:Models, Theoretical; D015203:Reproducibility of Results; D014611:Vaccination
keywords: CTL response; HIV-1 infection; Optimal control; Pontryagin maximum principle with delay