Viral load analysis of a biodynamical model of HIV-1 with unknown equilibrium points

The problem of feedback control for a class of the continuous differential equation models of the interaction dynamics of HIV-1 and CD4 and CD8 lymphocytes in the human body is investigated. The stabilizing controller is analogous to require only finite and little therapeutic drug regimen. The control law is derived such that in the closed-loop system, the states that represent CD4, CD8 and viral load, are regulated to a specified equilibrium point in the state space. Furthermore, the exact information about the equilibrium may not be available, although the CD4 and CD8 populations in a human have a typical range of equilibrium values. We propose a linear adaptation law and examine the conditions under which it achieves the stabilization of the unknown equilibrium.