HIV Infection Control Design With the Form of Constant or State Function

Abstract

Antiviral therapy widely used in HIV treatment has obtained some achievements in public health. In this study, an HIV infection dynamic mathematical model is considered and three types of the control strategy for this model are designed. On the basis of the Lyapunov theory, we propose three main theorems in which three types of the control strategy for drug treatments $u_{1}(t)$ or/and $u_{2} (t)$ are designed to push all states to the infection-free equilibrium point $E_{1}$ . Theorem 1 or Theorem 2 proposes the monotherapy with $u_{1} (t)$ only or with $u_{2} (t)$ only. The combination therapy with $u_{1}(t)$ and $u_{2} (t)$ together is constructed in Theorem 3 . In these three theorems, $u_{1}(t)$ or/and $u_{2} (t)$ can be a function of states or a fixed constant within a certain range. Finally, there are several simulation results to illustrate that the proposed controls are effective to treat the HIV infection. In the simulation section, there is a detailed discussion about the state responses with the proposed three types of control strategy for drug treatments.