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Adams, B., Banks, H., Davidian, M., Kwon, H.D., Tran, H., Wynne, S. and Rosenberg, E. (2005) HIV Dynamics: Modeling, Data Analysis, and Optimal Treatment Protocols. Journal of Computational and Applied Mathematics, 184, 10-49.
https://doi.org/10.1016/j.cam.2005.02.004

has been cited by the following article:

• 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.