In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDS
epidemic model with an imperfect HIV vaccine, varying total population size and
distributed time delay to become infectious due to intracellular delay between initial
infection of a cell by HIV and the release of new virions. Here, we have established some
sufficient conditions on the permanence and extinction of the disease by using inequality
analytical technique. We have obtained the explicit formula of the eventual lower bounds
of infected persons. We have introduced some new threshold values
R0 and R∗ and further obtained
that the disease will be permanent when R0 > 1 and the
disease will be going to extinct when R∗ < 1. By
Lyapunov functional method, we have also obtained some sufficient conditions for global
asymptotic stability of this model. The aim of the analysis of this model is to trace the
parameters of interest for further study, with a view to informing and assisting
policy-maker in targeting prevention and treatment resources for maximum
effectiveness.