Optimal Control of HIV Dynamic Using Embedding Method

Abstract

This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.

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.…”