Stability analysis for a HIV model with cell-to-cell transmission, two immune responses and induced apoptosis

In this paper, a dynamic HIV model with cell -to -cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non -negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R 0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease -free equilibrium, immune response -free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease -free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection.