Dynamical analysis of a latent HIV infection model with general incidence and multiple delays

In this paper, we propose a general latent HIV infection model with general incidence and three distributed delays. We start with the analysis of the proposed model by establishing the positivity and boundedness of solutions and calculating basic reproduction number R0. Then, we show that the infection-free equilibrium is globally asymptotically stable when R0<1 (is globally attractive when R0=1), while the disease is uniformly persistent when R0>1. In addition, the global stability of the infection equilibrium is also derived under certain conditions. Furthermore, we apply the geometric method to analyze the obtained characteristic equation and find that stability of the infection equilibrium may change in some special cases when the assumptions are not valid. Sensitive analysis is performed to investigate the dependence of R0 on parameters. Applications and numerical simulations are also in accordance with the qualitative results.