Analysis of an age-structured HIV infection model with logistic target-cell growth and antiretroviral therapy

This paper deals with the global dynamics of an age-structured human immunodeficiency virus infection model which incorporates a logistic growth term for the target cells and antiretroviral therapy. We perform some rigourous analyses for the model, including presenting an explicit formula for the reproductive number of the model, addressing the persistence of the solution semi-flow and the existence of a global attractor. Based on these analyses we establish some results on stability and instability for the system. The existence of Hopf bifurcation is also obtained around the positive equilibrium. Finally, some numerical examples are provided to illustrate our obtained results.