Mathematical analysis of an age-structured HIV model with intracellular delay

Abstract

<p style='text-indent:20px;'>In this paper, we study an age-structured HIV model with intracellular delay, logistic growth and antiretrowviral therapy. We first rewrite the model as an abstract non-densely defined Cauchy problem and obtain the existence of the unique positive steady state. Then through the linearization arguments we investigate the asymptotic behavior of steady states by determining the distribution of eigenvalues. We obtain successfully the globally asymptotic stability for the null equilibrium and (locally) asymptotic stability for the positive equilibrium respectively. Moreover, we also prove that Hopf bifurcations occur around the positive equilibrium under some conditions. In addition, we address the persistence of the semi-flow by showing the existence of a global attractor. Finally, some numerical examples are provided to illustrate the main results.</p>