Study on Mathematical Model of HIV-1 Dynamics with T Cell Activation

The most recent global health observatory data of HIV/AIDS published by WHO proclaims that
around 78 million people have been infected with the HIV virus and about 39 million people have
died of HIV virus. A deterministic in-host model of HIV-1 that incorporates naive and activated T
cells is being investigated. The model represents the dynamics of five subsets of T cells and one class
of HIV-1. The virus free and the infection persistent equilibria are found and their stability analysed.
With the aid of suitable Lyapunov functionals, we have shown that the model equilibria are globally
asymptotically stable under special conditions. The numerical simulation is performed to illustrate
both the short term and long term dynamics of HIV-1 infection. The results of simulation are in
agreement with published data with regard to CD4+ T cell concentration and the viral load.