title: Optimal control of HIV dynamic using embedding method.
abstract: This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.
authors.affiliation: Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 91775, Iran. zarei2003@yahoo.com
authors.forename: H
authors.initials: H
authors.lastname: Zarei
authors.forename: A V
authors.initials: AV
authors.lastname: Kamyad
authors.forename: M H
authors.initials: MH
authors.lastname: Farahi
mesh_terms: D000465:Algorithms; D019380:Anti-HIV Agents / Q000627:therapeutic use; D015496:CD4-Positive T-Lymphocytes / Q000276:immunology / Q000821:virology; D003198:Computer Simulation; D006678:HIV / Q000276:immunology; D015658:HIV Infections / Q000188:drug therapy* / Q000276:immunology* / Q000401:mortality / Q000821:virology; D054884:Host-Pathogen Interactions / Q000187:drug effects / Q000276:immunology; D006801:Humans; D008954:Models, Biological; D011382:Programming, Linear; D015996:Survival Rate
chemical_list: D019380:Anti-HIV Agents