Short and long period optimization of drug doses in the treatment of AIDS

Anais da Academia Brasileira de Ciências

Marco A. L. Caetano²  Takashi Yoneyama¹ 

[1] ,Universidade Estadual Paulista Matemática Aplicada e Computação Departamento de Estatística

关键词: modeling;    simulation;    drugs;    treatment;    AIDS;    modelamento;    simulação;    medicamentos;    tratamento;    AIDS;   

DOI  :  10.1590/S0001-37652002000300002

来源: SciELO

【 摘 要 】

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.

【 授权许可】

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