This paper studies the influence of apoptosis in the dynamics of the HIV infection. A new modeling of the healthy CD4+ T-cells activation-induced apoptosis is used. The parameters of this model are identified by using clinical data generated by monitoring patients starting Highly Active Anti-Retroviral Therapy (HAART). The sampling of blood tests is performed to satisfy the constraints of dynamical system parameter identification. The apoptosis parameter, which is inferred from clinical data, is then shown to play a key role in the early diagnosis of immunological failure.