Initiation of HIV Therapy

In this paper, we numerically show that the dynamics of the HIV system is sensitive to both the initial condition and the system parameters. These phenomena imply that the system is chaotic and exhibits a bifurcation behavior. To control the system, we propose to initiate an HIV therapy based on both the concentration of the HIV-1 viral load and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population. If the concentration of the HIV-1 viral load is higher than a threshold, then the first type of therapy will be applied. If the concentration of the HIV-1 viral load is lower than or equal to the threshold and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population is greater than another threshold, then the second type of therapy will be applied. Otherwise, no therapy will be applied. The advantages of the proposed control strategy are that the therapy can be stopped under certain conditions, while the state variables of the overall system is asymptotically stable with fast convergent rate, the concentration of the controlled HIV-1 viral load is monotonic decreasing, as well as the positivity constraint of the system states and that of the dose concentration is guaranteed to be satisfied. Computer numerical simulation results are presented for an illustration.