Using spectral methods on HIV infection with TAT and SSU72 activation.
HIV dynamics within the host are complex especially when a reservoir of latently infected CD4+ T cells are present. The failure of the immune system and antiviral therapy to suppress the virus has been suggested to be enhanced by the latently infected CD4+ T cells which are responsible for persistence of HIV within the host. Cells remaining in latent state have been shown to lack suffcient levels of Tat and associated activation-dependent host factor that are necessary for processive transcription of the virus. Tat is a protein that is capable of activating the latently infected CD4+ T cells. Recently, as a protein, Ssu72 was found to be responsible for activation and replication of the virus. Ssu72 enhances the effects of Tat activation in a mutualistic interactive manner. The interaction of Tat and Ssu72 thus, enhances the activation of the latently infected CD4+ T cells which may in turn expose the virus for possible attack by the immune system reaction. In the current study, we modify a constant virus HIV model to incorporate the effects of Tat and Ssu72 on latently infected CD4+ T cells. We analyze the models using both analytic and numerical techniques. Important threshold was derived and model analysis carried out. The incorporation of Tat and Ssu72 proteins on the HIV-1 model with a constant virus shows that, with time the unifected and infectious classes decrease to zero for a threshold value of 30-40 copies of each protein.