Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells

作     者：Purity M. Ngina Rachel Waema Mbogo Livingstone S. Luboobi 

作者机构：Strathmore Institute of Mathematical Sciences Strathmore University Nairobi Kenya 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2017年第8卷第8期

页      面：1153-1179页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：HIV Endemic Equilibrium Global Stability In-Vivo Disease-Free Equilibrium Basic Reproductive Number Backward Bifurcation 

摘      要：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 1 and unstable otherwise. The results show that at acute infection the CD8+ 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.