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

Zindoga Mukandavire; Christinah Chiyaka; Winston Garira; Godfrey Musuka

doi:10.1016/j.na.2008.11.026

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 journal › Article › peer-review

26 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 language	English
Pages (from-to)	1082-1093
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	3-4
DOIs	https://doi.org/10.1016/j.na.2008.11.026
Publication status	Published - 1 Aug 2009
Externally published	Yes

Keywords

Delay
HIV/AIDS model
Permanence
Persistence
Reproductive number
Stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

UN SDGs

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

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10.1016/j.na.2008.11.026

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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.",

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AU - Mukandavire, Zindoga

AU - Chiyaka, Christinah

AU - Garira, Winston

AU - Musuka, Godfrey

PY - 2009/8/1

Y1 - 2009/8/1

N2 - 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.

AB - 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.

KW - Delay

KW - HIV/AIDS model

KW - Permanence

KW - Persistence

KW - Reproductive number

KW - Stability

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 3-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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