In this paper, we consider a fourdimensional version of a human immunodeficiency virus (HIV) infection model, which is an extension of some previous threedimensional models. We approach the treatment problem by adding two controls u1 and u2 to the system for inhibiting viral production and preventing new infections. In fact, u1 is added to components of uninfected and infected cells to represent the effect of chemotherapy on the interaction of uninfected CD4+ T cells with infected cells. u2 is considered in the effector immune component as immunotherapy. The purpose of this work is to control the progress of the disease in a steady state. Hence, first, we obtain a relation between the two controls u1 and u2 such that a Hopf bifurcation occurs. Next, the Pontryagin minimum principle will be applied to derive the optimal therapy for HIV. At the end, numerical results are presented. The purpose of this work is to control the progress of the disease in a steady state. Hence, first, we obtain a relation between the two controllers u1 and u2 such that a Hopf bifurcation occurs.
Next, the Pontryagin minimum principle will be applied to derive the optimal therapy for HIV. In addition, we estimate the maximum possible numbers of switching of the controls, which is related
to the estimation of the numbers of zeros of the switching functions. At the end numerical results are presented.
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