Global analysis of an HIV/AIDS epidemic model

Zindoga Mukandavire; Prasenjit Das; Christinah Chiyaka; Farai Nyabadza

Global analysis of an HIV/AIDS epidemic model

Zindoga Mukandavire, Prasenjit Das, Christinah Chiyaka, Farai Nyabadza

Research output: Contribution to journal › Article › peer-review

18 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 language	English
Pages (from-to)	231-240
Number of pages	10
Journal	World Journal of Modelling and Simulation
Volume	6
Issue number	3
Publication status	Published - Aug 2010
Externally published	Yes

Keywords

Equilibria
HIV/AIDS model
Reproductive number
Stability

ASJC Scopus subject areas

Modeling and Simulation
General Engineering

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Cite this

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AU - Mukandavire, Zindoga

AU - Das, Prasenjit

AU - Chiyaka, Christinah

AU - Nyabadza, Farai

PY - 2010/8

Y1 - 2010/8

N2 - 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.

AB - 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.

KW - Equilibria

KW - HIV/AIDS model

KW - Reproductive number

KW - Stability

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AN - SCOPUS:77955945513

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IS - 3

ER -

Global analysis of an HIV/AIDS epidemic model

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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