TITLE:
Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells
AUTHORS:
Purity M. Ngina, Rachel Waema Mbogo, Livingstone S. Luboobi
KEYWORDS:
HIV, Endemic Equilibrium, Global Stability In-Vivo, Disease-Free Equilibrium, Basic Reproductive Number, Backward Bifurcation
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
25,
2017
ABSTRACT: There have been many mathematical models aimed at analysing the in-vivo
dynamics of HIV. However, in most cases the attention has been on the interaction
between the HIV virions and the CD4+ T-cells. This paper brings in
the intervention of the CD8+ T-cells in seeking, destroying, and killing the infected
CD4+ T-cells during early stages of infection. The paper presents and
analyses a five-component in-vivo model and applies the results in investigating
the in-vivo dynamics of HIV in presence of the CD8+ T-cells. We prove
the positivity and the boundedness of the model solutions. In addition, we
show that the solutions are biologically meaningful. Both the endemic and virions-
free equilibria are determined and their stability investigated. In addition,
the basic reproductive number is derived by the next generation matrix
method. We prove that the virions-free equilibrium state is locally asymptotically
stable if and only if R0 + T-cells play a paramount role in reducing
HIV viral replication. We also observe that the model exhibits backward and
trans-critical bifurcation for some set of parameters for R0 . This is a clear
indication that having R0 is not sufficient condition for virions depletion.