OPTIMAL CONTROL OF HAART AND IL-2 IMMUNOTHERAPY IN CD4+T CELLS RESPONSE FOR HIV INFECTION

In this paper we investigate optimal control problem in case of applying therapies against human immunodeficiency virus (HIV) including two therapeutic factors - highly active anti-retroviral therapy (HAART) and cytokine interleukin-2 (IL-2). The dynamics of HIV spread is described with the three-dimensional system of ordinary differential equations. In this study we consider two controls, each of them corresponds to amount of dose in case of applying HAART drugs and IL-2, respectively. This system for constant control parameters was described and analysed in our previous work. Our aim is minimising the cost of both controls (side effects) and minimising the number of HIV-infected cells as well. In order to do that, we conducted numerical analysis, using the approach "First Discretize then Optimize" . We consider two cases - in the first one we assume that controls are time-dependent functions; in the second case we take the constant controls equal to the mean-value of optimal ones. Comparing them, we stated that the treatment reflecting the first scenario is better than the treatment corresponding to the second one.