Mathematical analysis of multi-target cells and multi-strain age-structured model with two HIV infection routes

In this paper, we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infected cells, multiple target cells (Langerhans-cells and CD4(+) T-cells), multiple viral strains (CCR5 and CXR4 HIV) and multiple infection routes (cell-to-cell and cell-to-virus). The basic reproduction number, R-0, of the whole model is derived from two transmission mechanisms: one is the potential trigger from the infection routes for a single target cell and other is the joint effect of multiple viral infections for multi-target cells. Accordingly, we study the global stability of the steady states for the single target model. For the whole model, we prove that the infection-free steady state is globally asymptotically stable if R-0 < 1, whereas viruses persist uniformly if R-0 > 1. Numerical simulations are carried out to illustrate the theoretical results. Sensitive analyses expound the effect of model parameters on the comprehensive reproduction number. It is remarkable to find that simultaneous control of HIV infection for two target cells can effectively reduce the viral loads within-host. Finally, our work suggests that the synergetic mechanism of multi-target cells and multi-strain cannot be ignored during treatment.