Dynamics of two time delays differential equation model to HIV latent infection

In this paper, we studied a HIV latent infection model with two time delays, where one delay is the time between viral entry into a cell and establishment of HIV latency and the other delay is the time between cell infection and viral production. The infection usually considered is linear, but in this article we consider that the infection rate of modeling HIV infection is nonlinear, where the rate of infection is βTV1+bV, and logistic growth of the uninfected target cells T. We defined the basic reproductive number and showed the local and global stability of the disease-free equilibrium and the permanence of the infected equilibrium. Furthermore, we discussed the dynamics of system under the three conditions: (1) τ1=τ2=0, (2) τ1=0,τ2>0, (3) τ1>0,τ2∈[0,τ2∗).