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

Z. Mukandavire; W. Garira; C. Chiyaka

doi:10.1016/j.jmaa.2006.07.102

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

Z. Mukandavire, W. Garira, C. Chiyaka

National University of Science and Technology

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

76 Citations (Scopus)

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 language	English
Pages (from-to)	916-933
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	330
Issue number	2
Early online date	12 Sept 2006
DOIs	https://doi.org/10.1016/j.jmaa.2006.07.102
Publication status	Published - 15 Jun 2007

Keywords

Delay
Global stability
HIV/AIDS model
Incubation
Lyapunov functional
Persistence

UN SDGs

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

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http://www.mendeley.com/research/asymptotic-properties-hivaids-model-time-delay

Cite this

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AU - Mukandavire, Z.

AU - Garira, W.

AU - Chiyaka, C.

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Y1 - 2007/6/15

N2 - 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.

AB - 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.

KW - Delay

KW - Global stability

KW - HIV/AIDS model

KW - Incubation

KW - Lyapunov functional

KW - Persistence

U2 - 10.1016/j.jmaa.2006.07.102

DO - 10.1016/j.jmaa.2006.07.102

M3 - Article

SN - 1096-0813

VL - 330

SP - 916

EP - 933

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

Abstract

Keywords

UN SDGs

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