Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010Ecology (Part 2)
|70 - 95
|08 April 2010
Analysis of a Nonautonomous HIV/AIDS Model
Mathematical Institute, Slovak Academy of Sciences Stefanikova
* Present address: Department of Mathematics, Bengal
Engineering and Science University, Shibpur, Howrah-711103, India. E-mail:
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.
Mathematics Subject Classification: 92D25 / 92D30 / 34D23
Key words: HIV/AIDS / time delay / permanence / extinction / Lyapunov functional / global stability
© EDP Sciences, 2010
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