title: Short and long period optimization of drug doses in the treatment of AIDS.
abstract: Numerical optimization techniques are useful in solving problems of computing the best inputs for systems described by mathematical models and when the objectives can be stated in a quantitative form. This work concerns the problem of optimizing the drug doses in the treatment of AIDS in terms of achieving a balance between the therapeutic response and the side effects. A mathematical model describing the dynamics of HIV viruses and CD4 cells is used to compute the short term optimal drug doses in the treatments of patients with AIDS by a direct method of optimization using a cost function of Bolza type. The model parameters were fitted to actual published clinical data. In order to simplify the numerical procedures, the control law is expressed as a series and the sub-optimal control is obtained by truncating the higher terms. When the patient reaches a clinically satisfactory state, the LQR - Linear Quadratic Regulator technique is used to determine the long period maintenance doses for the drugs. The doses computed using the LQR technique tend to be smaller than equivalent constant-dose therapy in terms of increase in the counts of CD4+T cells and reduction of the density of free viruses.
authors.affiliation: Departamento de Estatística, Matemática Aplicada e Computação, Universidade Estadual Paulista, Rio Claro, SP, Brasil. maleonel@rc.unesp.br
authors.forename: Marco A L
authors.initials: MA
authors.lastname: Caetano
authors.forename: Takashi
authors.initials: T
authors.lastname: Yoneyama
mesh_terms: D000163:Acquired Immunodeficiency Syndrome / Q000188:drug therapy* / Q000276:immunology; D019380:Anti-HIV Agents / Q000008:administration & dosage* / Q000009:adverse effects; D018791:CD4 Lymphocyte Count; D015496:CD4-Positive T-Lymphocytes / Q000187:drug effects / Q000821:virology; D003198:Computer Simulation; D006678:HIV / Q000187:drug effects; D017320:HIV Protease Inhibitors / Q000008:administration & dosage / Q000009:adverse effects; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D018894:Reverse Transcriptase Inhibitors / Q000008:administration & dosage* / Q000009:adverse effects; D013997:Time Factors; D016896:Treatment Outcome
chemical_list: D019380:Anti-HIV Agents; D017320:HIV Protease Inhibitors; D018894:Reverse Transcriptase Inhibitors