Nonlinear MPC of HIV-1 infection with periodic inputs

Although many papers address the issue of therapy design for HIV-1 infection based on control methods, the results available in the literature do not in general consider the fact that the manipulated variable is not continuous but a train of pulses. In addition, they are usually concerned only with the relation between drug effect (assumed to be manipulated) and virus dynamics. In order to improve the direct relation with actual clinical practice, the present work takes as manipulated variable a train of impulses that represent the pills taken by the patient and includes pharmacokinetics (PK) and pharmacodynamic (PD) drug models. In addition, patient adherence to treatment and their impact on virus drug resistance is also modeled. The problem of driving the viral load to a low specified value while minimizing the amount of drugs administered to the patient is thus addressed by nonlinear model predictive control (NMPC) with periodic inputs. Therefore, the paper contributions consist in the characterization of the results obtained with this type of control strategy in a HIV-1 infection model comprising drug PK and PD, development of virus resistance to drugs and virus dynamics. Furthermore, it is shown that various amounts of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drugs can be given depending on the weights of the cost function minimized by periodic NMPC, while attaining the same control objective. It is proposed that these weights can be adjusted to minimize the toxicity of the drug cocktail administered.