title: Free terminal time optimal control problem of an HIV model based on a conjugate gradient method.
abstract: The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.
authors.affiliation: Department of Mathematics, Inha University, Yonghyundong, Namgu, Incheon, 402-751, Republic of Korea. iamnumber2@inha.ac.kr
authors.forename: Taesoo
authors.initials: T
authors.lastname: Jang
authors.forename: Hee-Dae
authors.initials: HD
authors.lastname: Kwon
authors.forename: Jeehyun
authors.initials: J
authors.lastname: Lee
mesh_terms: D019380:Anti-HIV Agents / Q000008:administration & dosage*; D015658:HIV Infections / Q000188:drug therapy* / Q000276:immunology / Q000821:virology; D015497:HIV-1; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013601:T-Lymphocytes / Q000187:drug effects / Q000276:immunology / Q000821:virology; D013997:Time Factors
chemical_list: D019380:Anti-HIV Agents