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Analysis of a Nonautonomous HIV/AIDS Model

Published online by Cambridge University Press:  08 April 2010

G. P. Samanta
G. P. Samanta*
Affiliation:
Mathematical Institute, Slovak Academy of Sciences Stefanikova 49, 81473 Bratislava, Slovak Republic
*
* Present address: Department of Mathematics, BengalEngineering and Science University, Shibpur, Howrah-711103, India. E-mail:g_p_samanta@yahoo.co.uk
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Abstract

In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDSepidemic model with an imperfect HIV vaccine, varying total population size anddistributed time delay to become infectious due to intracellular delay between initialinfection of a cell by HIV and the release of new virions. Here, we have established somesufficient conditions on the permanence and extinction of the disease by using inequalityanalytical technique. We have obtained the explicit formula of the eventual lower boundsof infected persons. We have introduced some new threshold valuesR 0 and R ∗ and further obtainedthat the disease will be permanent when R 0 > 1 and thedisease will be going to extinct when R ∗ < 1. ByLyapunov functional method, we have also obtained some sufficient conditions for globalasymptotic stability of this model. The aim of the analysis of this model is to trace theparameters of interest for further study, with a view to informing and assistingpolicy-maker in targeting prevention and treatment resources for maximumeffectiveness.

Keywords

HIV/AIDStime delaypermanenceextinctionLyapunov functionalglobal stability

Information

Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 6: Ecology (Part 2) , 2010 , pp. 70 - 95
Copyright
© EDP Sciences, 2010

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