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

M. Kgosimore, E. M. Lungu

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 R0t < R0, R 0t < R0v and γeRVT(σ) < RUT(α), where R0t and R0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R0 is the basic reproduction number in the absence of any intervention, RUT(α) and R VT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) 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 R0t < R0, R0t < R0v and γeRVT(σ) < RUT(α) are satisfied.

Original languageEnglish
Pages (from-to)399-417
Number of pages19
JournalJournal of Biological Systems
Volume12
Issue number4
DOIs
Publication statusPublished - Dec 1 2004

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Vaccination
vaccination
acquired immune deficiency syndrome
human immunodeficiency virus
Equilibrium Point
Acquired Immunodeficiency Syndrome
HIV
Reproduction number
Endemic Equilibrium
Stability of Equilibria
Asymptotically Stable
Reproduction
Therapeutics
effect
programme

All Science Journal Classification (ASJC) codes

  • Ecology
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this

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The effects of vaccination and treatment on the spread of HIV/AIDS. / Kgosimore, M.; Lungu, E. M.

In: Journal of Biological Systems, Vol. 12, No. 4, 01.12.2004, p. 399-417.

Research output: Contribution to journalArticle

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