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

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 in- 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 0 1 R < 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 0 1 R < . This is a clear indication that having 0 1 R < is not sufficient condition for virions depletion.

Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity

“…In immunology, bifurcations and multi-stability have been studied in the context of T cell differentiation [64,65], including the role of cytokines [66]. Ngina et al [67] have investigated the dynamics of HIV from the perspective of interactions between HIV virions and CD8 + T cells, and identified a region of bi-stability associated with the backward bifurcation, where the system can reach either a virion-free or endemic equilibrium depending on the initial conditions. This observation has profound implications for developing an effective anti-retroviral therapy.…”

An efficient method to solve the mathematical model of HIV infection for CD8+ T-cells

“…According to the recent enumeration, more than 35 million people have been died by HIV virous and more than 37 million people carry this virous in their body and they are living as a menace on the world. Also, they can transmit this threat by having unprotected sex, forwarding from mother to child and other ways [35,37,47,53].…”

TheIn VivoDynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells

“…During the initial infection stage, high level of viral replication takes place lasting for about three to six weeks upon infection [ 3 ]. This period is followed by the asymptomatic stage which is characterized by high level of immune response; this helps in stabilizing the viral load in the infected person.…”

“…Ngina et al [ 3 ] analyzed a five-dimensional in-host model. The results from the study established the importance of the CD8 + T-cells in controlling HIV viral progression.…”

“…This study wishes to improve the research by Ngina et al [ 3 ] by introducing the wild type and and the resistant CD4 + T-cells. The study will also be aimed at addressing the gaps noted from the cited literature.…”