A Closed-Loop Approach to Antiretroviral Therapies for HIV Infection

Abstract

Antiretroviral therapies allowing for regular medical intervention in an optimal feedback role are substantiated. Individual therapies are evaluated from a multi-objective cost perspective, under different time and history constrains. The dynamics of the control system is governed by three state variables: healthy T-cells, infected T-cells, and viral particles. The drug dose administrated to the patient is taken as the manipulated or control variable. Illustrations of the methodology employed are provided for a fixed time-horizon of 180 days and variable prescription intervals, inverse discount factors, state discretization, and thresholds. Two cases are discussed: (i) beginning of the infection and (ii) near endemic equilibrium. Both open-loop and closed-loop results are presented. Dynamic Programming has been employed in the numerical treatment of the problem. Safety recommendations are also designed to cope with the chaotic behavior of the free dynamics’ flow in critical regions of the states’ domain. A software package is envisioned to assist physicians in assessing the patient ‘‘state’’, estimating antiretroviral dose prescriptions for the whole treatment period, simulating the patient’s evolution, eventually correcting the original sequence in presence of incoming data, and evaluating combined costs of alternative treatment strategies.