Threshold dynamics of a general delayed HIV model with double transmission modes and latent viral infection

In this paper, a general HIV model incorporating intracellular time delay is investigated. Taking the latent virus infection, both virus-to-cell and cell-to-cell transmissions into consideration, the model exhibits threshold dynamics with respect to the basic reproduction number ${\mathfrak{R}}_0$. If ${\mathfrak{R}}_0<1$, then there exists a unique infection-free equilibrium $E_0$, which is globally asymptotically stable. If ${\mathfrak{R}}_0>1$, then there exists $E_0$ and a globally asymptotically stable infected equilibrium $E^{\ast }$. When ${\mathfrak{R}}_0=1$, $E_0$ is linearly neutrally stable and a forward bifurcation takes place without time delay around ${\mathfrak{R}}_0=1$. The theoretical results and corresponding numerical simulations show that the existence of latently infected cells and the intracellular time delay have vital effect on the global dynamics of the general virus model.