Asymptotic properties of an HIV/AIDS model with a time delay

Z. Mukandavire, W. Garira, C. Chiyaka

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Abstract

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)916-933
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume330
Issue number2
Early online date12 Sep 2006
DOIs
Publication statusPublished - 15 Jun 2007

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Keywords

  • Delay
  • Global stability
  • HIV/AIDS model
  • Incubation
  • Lyapunov functional
  • Persistence

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