On the complexities of modeling HIV/AIDS in Southern Africa

F. Nyabadza

doi:10.3846/1392-6292.2008.13.539-552

On the complexities of modeling HIV/AIDS in Southern Africa

F. Nyabadza

Stellenbosch University

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

3 Citations (Scopus)

Abstract

In this paper problems associated with the modeling of HIV/AIDS in Southern Africa are presented. A mathematical model is presented to highlight the three major challenges of modeling HIV/AIDS, i.e condom use, vertical transmission and treatment. The model analysis for the case, where the treatment parameter p = 0, is presented in terms of the model reproduction number R and threshold parameters R_r and R_A that show the contribution of vertical transmission. It is shown that if R, R_T, R_A < 1, then the disease free equilibrium point is both locally asymptotically and globally stable. Numerical simulations for the model are presented to determine the role of some key epidemiological parameters of the model.

Original language	English
Pages (from-to)	539-552
Number of pages	14
Journal	Mathematical Modelling and Analysis
Volume	13
Issue number	4
DOIs	https://doi.org/10.3846/1392-6292.2008.13.539-552
Publication status	Published - 2008
Externally published	Yes

Keywords

Complexities
Equilibrium points
Interventions
Reproduction number
Stability

ASJC Scopus subject areas

Analysis
Modeling and Simulation

UN SDGs

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

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10.3846/1392-6292.2008.13.539-552

Cite this

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AB - In this paper problems associated with the modeling of HIV/AIDS in Southern Africa are presented. A mathematical model is presented to highlight the three major challenges of modeling HIV/AIDS, i.e condom use, vertical transmission and treatment. The model analysis for the case, where the treatment parameter p = 0, is presented in terms of the model reproduction number R and threshold parameters Rr and RA that show the contribution of vertical transmission. It is shown that if R, RT, RA < 1, then the disease free equilibrium point is both locally asymptotically and globally stable. Numerical simulations for the model are presented to determine the role of some key epidemiological parameters of the model.

KW - Complexities

KW - Equilibrium points

KW - Interventions

KW - Reproduction number

KW - Stability

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JO - Mathematical Modelling and Analysis

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ER -

On the complexities of modeling HIV/AIDS in Southern Africa

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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