Optimal Control of HIV-Virus Dynamics

Abstract

In this paper we consider a mathematical model of HIV-virus dynamics and propose an efficient control strategy to keep the number of HIV virons under a pre-specified level and to reduce the total amount of medications that patients receive. The model considered is a nonlinear third-order model. The third-order model describes dynamics of three most dominant variables: number of healthy white blood cells (T-cells), number of infected T-cells, and number of virus particles. There are two control variables in this model corresponding to two categories of antiviral drugs: reverse transcriptase inhibitors (RTI) and protease inhibitors (PI). The proposed strategy is based on linearization of the nonlinear model at the equilibrium point (steady state). The corresponding controller has two components: the first one that keeps the system state variables at the desired equilibrium (set-point controller) and the second-one that reduces in an optimal way deviations of the system state variables from their desired equilibrium values. The second controller is based on minimization of the square of the error between the actual and desired (equilibrium) values for the linearized system (linear-quadratic optimal controller). The obtained control strategy recommends to HIV researchers and experimentalists that the constant dosages of drugs have to be administrated at all times (set point controller, open-loop controller) and that the variable dosages of drugs have to be administrated on a daily basis (closed-loop controller, feedback controller).

Observer-Based Output Feedback Linearization Control with Application to HIV Dynamics

“…The main control objectives are: 27,38 • Decreasing the viral load to 10% of its initial value within eight weeks.…”

“…Having the HIV infection dynamics, different control approaches can be used for reducing the viral load and increasing the healthy white blood cells (T-cells). For instance, optimal control, ,,− model predictive control (MPC), − global linearizing control (GLC), ,− sliding mode control, and fuzzy control − have been examined in many research works. In what follows, some of these works are reviewed briefly.…”

Nonlinear and Robust Control Strategy Based on Chemotherapy to Minimize the HIV Concentration in Blood Plasma

“…Additionally, the HIV mathematical modeling has allowed the analysis of the dynamic behavior of the virus infection, which has helped to propose regulation strategies to diminish indirectly the viral concentration [9][10][11]. An increasing number of works in the literature deal with the HIV virus regulation via control approaches and reduced HIV models [12][13][14][15][16][17][18][19][20]. Kim et al [21] found through a bifurcation analysis the range of optimal constant drug dosing for the reverse transcription inhibitor and the protease inhibitor in order to achieve LTNP in HIV patients.…”

Nonlinear Uncertain HIV-1 Model Controller by Using Control Lyapunov Function

“…Based on data provided in [5], many viral dynamics that can not only give the kinetics dynamic of HIV-1 disease but also give guidelines to develop new treatment strategy are investigated. Controlling HIV infection disease has been an interesting problem for many researchers [6][7][8][9][10][11]. It is well known [12,13] that a control Lyapunov function, if available, will be a convenient tool to analyze stability, evaluate the system's robustness to perturbations, or even to modify the design to enhance robustness or performance [14].…”