Global analysis of an HIV/AIDS epidemic model

Zindoga Mukandavire, Prasenjit Das, Christinah Chiyaka, Farai Nyabadza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We present an HIV/AIDS epidemic model that incorporates constant recruitment and sexually active AIDS individuals. The disease-free and endemic equilibria are found and their local as well as global stabilities are investigated. Using a Lyapunov function and LaSalle's invariant set theorem, we proved that the disease-free equilibrium is globally asymptotically stable. Local stability of the endemic equilibrium is determined using the center manifold theory and using the Poincarè-Bendixson property, global asymptotic stability is proved.

Original languageEnglish
Pages (from-to)231-240
Number of pages10
JournalWorld Journal of Modelling and Simulation
Volume6
Issue number3
Publication statusPublished - 1 Aug 2010
Externally publishedYes

Fingerprint

Endemic Equilibrium
Global Analysis
Epidemic Model
Local Stability
Center Manifold
Globally Asymptotically Stable
Global Asymptotic Stability
Invariant Set
Lyapunov functions
Asymptotic stability
Global Stability
Lyapunov Function
Theorem

Keywords

  • Equilibria
  • HIV/AIDS model
  • Reproductive number
  • Stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)

Cite this

Global analysis of an HIV/AIDS epidemic model. / Mukandavire, Zindoga; Das, Prasenjit; Chiyaka, Christinah; Nyabadza, Farai.

In: World Journal of Modelling and Simulation, Vol. 6, No. 3, 01.08.2010, p. 231-240.

Research output: Contribution to journalArticle

Mukandavire, Z, Das, P, Chiyaka, C & Nyabadza, F 2010, 'Global analysis of an HIV/AIDS epidemic model' World Journal of Modelling and Simulation, vol. 6, no. 3, pp. 231-240.
Mukandavire, Zindoga ; Das, Prasenjit ; Chiyaka, Christinah ; Nyabadza, Farai. / Global analysis of an HIV/AIDS epidemic model. In: World Journal of Modelling and Simulation. 2010 ; Vol. 6, No. 3. pp. 231-240.
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