On the design of human immunodeficiency virus treatment based on a non-linear time-delay model

Mathematical modelling and methods from control theory can be employed to find appropriate drug regimens in human immunodeficiency virus (HIV) treatment. In this study, using a non-linear time-delay model, the authors design some suboptimal highly active antiretroviral therapy (HAART) [http://www.en.wikipedia.org/wiki/Protease_inhibitor_%28pharmacology%29] regimens for patients with HIV. The non-linear delayed model is used to describe the dynamical interactions between HIV and human immune system in the presence of HAART. Based on the model, a set point tracking problem is defined in order to set the number of susceptible CD4⁺T cells to a desired value. To solve this set point tracking problem in a suboptimal way, the authors introduce a new method which is able to consider constraints on the amount of drug dosage. It is proved that the proposed method is able to set the number of susceptible CD4⁺T cells to the desired value. Simulation results confirm that the method is efficient even in the presence of parametric uncertainties.