Table of Contents
International Scholarly Research Notices
Volume 2017 (2017), Article ID 2124789, 10 pages
Research Article

The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells

Institute of Mathematical Sciences, Strathmore University, P.O. Box 59857, Nairobi 00200, Kenya

Correspondence should be addressed to Purity Ngina

Received 19 June 2017; Revised 25 September 2017; Accepted 15 October 2017; Published 14 November 2017

Academic Editor: Shengqiang Liu

Copyright © 2017 Purity Ngina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having . Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.