Asymptotic dynamics for an age-structured HIV model with two delays

This paper deals with an age-structured HIV model with antiretrowviral therapy and two infection routes (virus-to-cell and cell-to-cell). The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Based on the existence of equilibria, the global asymptotical stability of the disease-free equilibrium is studied by applying theory of operator semigroups and spectral analysis. The stability and Hopf bifurcation results with two delays around the endemic equilibrium are also well described under some conditions by the geometric stability switch criteria. Finally some numerical examples are presented to illustrate the obtained results.