Using spectral methods on HIV infection with TAT and SSU72 activation.
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Date
2016
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Abstract
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.
Description
Master of Science in Applied Mathematics.
Keywords
HIV infections--Mathematical models., Spectral sequences (Mathematics), T cells--Receptors., Phosphoprotein phosphatases., Theses--Mathematics.