Analysis of an age-structured HIV infection model with cell-to-cell transmission

Though cell-to-cell transmission cannot be overlooked in HIV infection, many existing studies have only focused on the cell-free infection. Moreover, the infection rate is an important factor affecting viral transmission. Considering general incidence rates and latently infected cells, we develop an age-structured model with the two transmission modes. The expression of the basic reproduction number is derived. It turns out that the existence and local stability of equilibria is determined by the basic reproduction number. Before establishing the global dynamical behavior, we prove the existence of compact global attractors and uniform persistence. Then, by using the fluctuation lemma and Lyapunov functionals, a threshold dynamics is obtained. Saturated incidence rates are selected to simulate the relationship between latently infected cells and viruses, as well as the role of age-dependent parameters in infection.