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In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number  R  0 , the CTL immune response reproduction number  R  1   z  , the antibody immune response reproduction number  R  1   w  , the antibody immune competition reproduction number  R  2   w  , and the CTL immune response competition reproduction number  R  3   z  . On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for  R  0  is performed in order to check the impact of different input parameters.

Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity