A new mathematical model is proposed to describe the interaction between the virus and the immune cells in an HIV infected host. For this new model, we study the existence of non-negative equilibria, bifurcation of equilibria, and stability of equilibria. We also carry out numerical simulations to illustrate all possible dynamics. In addition, we numerically explore drug therapy treatment strategies to find the right regimes for the strengths of the therapy and the duration of the treatment so that sustained immunity can be established.
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