Analysis of a Nonautonomous HIV/AIDS Model

Mathematical Institute, Slovak Academy of Sciences Stefanikova 49, 81473 Bratislava, Slovak Republic

^* Present address: Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, India. E-mail: g_p_samanta@yahoo.co.uk

Abstract

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.