Optimal control and feedback control problem with biological applications

초록

We introduce a rather large variety of optimal control problems to derive optimal dynamic multidrug therapies for human immunodeficiency virus (HIV) type 1 infection. In this context, we describe optimal and feedback tracking problem attempting to drive the states of the system to a ”healthy” stationary state in which the viral load is low and the immune response is strong. We also consider a free terminal tracking problem the to suggest the minimum durations of treatment as well as the optimal treatment schedules for HIV patients to reach to a healthy state. We demonstrate by numerical simulations that by anticipation of and response to the disease progression, the dynamic multidrug strategy reduces the viral load, increases the CD4+ T-cell count and improves the immune response.