Optimal drug scheduling for HIV therapy efficiency improvement

Abstract The purpose of the paper is to use numerical analysis and optimisation tools developed for applied mechanic research to suggest improved therapies to try and cure HIV infection. The evolution of the infection is modelled by an ordinary differential equation system which includes both immune response and multi-drug effects. For a fixed time, one looks for a two-drug treatment strategy based on Pontryagin’s minimum principle. Basically, the method applied in this paper can be considered as an optimal control one, where drug dose effects are regarded as control inputs. The quadratic objective function considered takes into account three contributions: the viral load, the transient evolution of infection and the percentage of efficiency of drug used. Simulations are carried out using an indirect optimisation method. At each step the differential system is solved using Runge–Kutta scheme. The effectiveness of drug is assumed to be fully controlled by drug dose level. Results based on an high drug dose strength ratio hypothesis highlight that a progressive reduction of reverse transcriptase inhibitor drug dose on the one hand along with, on the other hand, a progressive increase of protease inhibitor one is needed for optimality in common cases. The possibility of improving scheduled interrupted treatment which has lacked benefits and moreover has appeared to be harmful in clinical trials so far, is then examined.