The effects of vaccination and treatment on the spread of HIV/AIDS

Journal article

Authors / Editors

Lungu, Edward

Research Areas

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Publication Details

Author list: Kgosimore M, Lungu EM

Publisher: World Scientific Publishing

Place: SINGAPORE

Publication year: 2004

Journal: Journal of Biological Systems (0218-3390)

Journal acronym: J BIOL SYST

Volume number: 12

Issue number: 4

Start page: 399

End page: 417

Number of pages: 19

ISSN: 0218-3390

eISSN: 1793-6470

Languages: English-Great Britain (EN-GB)

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Abstract

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R-0t < R-0, R-0t < R-0nu and gamma(e) R-VT (sigma) < R-UT (alpha), where R-0t and R-0nu are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R-0 is the basic reproduction number in the absence of any intervention, R-UT(alpha) and R-VT(sigma) are respectively the reproduction numbers in the presence of a treatment (alpha) and a combination of vaccination and treatment (sigma) strategies. Secondly, that if R < 1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R > 1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R = 1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R-0t < R-0, < R-0nu < R-0nu and gamma(e) R-VT(sigma) < R-UT(alpha) are satisfied.

Keywords

endemic, HIV/AIDS, reproduction number, treatment, vaccination

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