Abstract
This paper proposes and investigates an HIV dynamics model with adaptive immunity. The model describes the interactions between five compartments: healthy CD4(+)T cells, silent infected cells, active infected cells, free HIV particles, and cytotoxic T lymphocytes and antibodies. The model incorporates two methods of transmission: virus-to-cell and cell-to-cell (CTC). The healthy cells can be infected when they come into contact with free HIV particles or silent infected cells or active infected cells. We established that the model is well-posed by establishing the nonnegativity and boundedness of the solutions. The model has admitted five equilibria, and their existence is governed by five threshold parameters. We prove the global asymptotic stability of the equilibria by constructing Lyapunov functions. We have illustrated the theoretical results by numerical simulations. We have shown that the inclusion of CTC transmission decreases the concentration of healthy cells and increases the concentration of free HIV particles.