title: Fuzzy modeling and control of HIV infection.
abstract: The present study proposes a fuzzy mathematical model of HIV infection consisting of a linear fuzzy differential equations (FDEs) system describing the ambiguous immune cells level and the viral load which are due to the intrinsic fuzziness of the immune system's strength in HIV-infected patients. The immune cells in question are considered CD4+ T-cells and cytotoxic T-lymphocytes (CTLs). The dynamic behavior of the immune cells level and the viral load within the three groups of patients with weak, moderate, and strong immune systems are analyzed and compared. Moreover, the approximate explicit solutions of the proposed model are derived using a fitting-based method. In particular, a fuzzy control function indicating the drug dosage is incorporated into the proposed model and a fuzzy optimal control problem (FOCP) minimizing both the viral load and the drug costs is constructed. An optimality condition is achieved as a fuzzy boundary value problem (FBVP). In addition, the optimal fuzzy control function is completely characterized and a numerical solution for the optimality system is computed.
authors.affiliation: Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, Iran. zarei2003@yahoo.com
authors.forename: Hassan
authors.initials: H
authors.lastname: Zarei
authors.forename: Ali Vahidian
authors.initials: AV
authors.lastname: Kamyad
authors.forename: Ali Akbar
authors.initials: AA
authors.lastname: Heydari
mesh_terms: D019380:Anti-HIV Agents / Q000191:economics / Q000627:therapeutic use; D015496:CD4-Positive T-Lymphocytes / Q000187:drug effects / Q000276:immunology / Q000821:virology; D017143:Fuzzy Logic; D015658:HIV Infections / Q000188:drug therapy / Q000276:immunology*; D006801:Humans; D018448:Models, Immunological; D013602:T-Lymphocytes, Cytotoxic / Q000187:drug effects / Q000276:immunology / Q000821:virology; D019562:Viral Load / Q000187:drug effects / Q000276:immunology
chemical_list: D019380:Anti-HIV Agents