About 78 million people have been infected with the HIV virus and about 39 million people have died from the HIV virus, according to the most recent World Health Observatory HIV/AIDS data released by the WHO. A deterministic HIV-1 in-host model combining naive and activated T cells is being studied. The model reflects the dynamics of five T cell subsets and one HIV-1 class. The virus-free and persistent equilibria of the infection are found and their stability is analysed. We have demonstrated that the model equilibria are globally asymptotically stable under special conditions with the help of appropriate Lyapunov functionals. The computational simulation is done to demonstrate both the dynamics of HIV-1 infection in the short and long term. The simulation results are consistent with published data with regard to the concentration of CD4+ T cells and the viral load.

**Author(s) Details**

**Obias Mulenga Chimbola
**Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana and Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/339