Mathematical analysis of a sex-structured HIV/AIDS model with a discrete time delay

Zindoga Mukandavire, Christinah Chiyaka, Winston Garira, Godfrey Musuka

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

A sex-structured mathematical model for heterosexual transmission of HIV/AIDS with explicit incubation period is presented as a system of discrete delay differential equations. The epidemic threshold and equilibria for the model are determined and stabilities are examined. The disease-free equilibrium is shown to be locally and globally stable when the basic reproductive number R0 is less than unity. We use the Lyapunov functional approach to show that the endemic equilibrium is locally asymptotically stable. Further comprehensive qualitative analysis of the model including persistence and permanence are investigated.

Original languageEnglish
Pages (from-to)1082-1093
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number3-4
DOIs
Publication statusPublished - 1 Aug 2009
Externally publishedYes

Fingerprint

Mathematical Analysis
Time delay
Discrete-time
Basic Reproductive number
Discrete Delay
Endemic Equilibrium
Permanence
Lyapunov Functional
Qualitative Analysis
Asymptotically Stable
Delay Differential Equations
Persistence
Differential equations
Mathematical Model
Mathematical models
Model

Keywords

  • Delay
  • HIV/AIDS model
  • Permanence
  • Persistence
  • Reproductive number
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Mathematical analysis of a sex-structured HIV/AIDS model with a discrete time delay. / Mukandavire, Zindoga; Chiyaka, Christinah; Garira, Winston; Musuka, Godfrey.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 71, No. 3-4, 01.08.2009, p. 1082-1093.

Research output: Contribution to journalArticle

Mukandavire, Zindoga ; Chiyaka, Christinah ; Garira, Winston ; Musuka, Godfrey. / Mathematical analysis of a sex-structured HIV/AIDS model with a discrete time delay. In: Nonlinear Analysis, Theory, Methods and Applications. 2009 ; Vol. 71, No. 3-4. pp. 1082-1093.
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