Mat hematical analysis of multi-target cells and multi-strnin 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 infectedcells,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).Thebasic reproduction number,R_(0),of the whole model is derived from two transmissionmechanisms:one is the potential trigger from the infection routes for a single target celland 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 thewhole model,we prove that the infection-free steady state is globally asymptoticallystable if R_(0)<1,whereas viruses persist uniformly if R_(0)>1.Numerical simulations arecarried out to illustrate the theoretical results.Sensitive analyses expound the effect ofmodel parameters on the comprehensive reproduction number.It is remarkable to findthat simultaneous control of HlV infection for two target cells can effectively reducethe viral loads within-host.Finally,our work suggests that the synergetic mechanism ofmulti-target cells and multi-strain cannot be ignored during treatment.