Effect of a preventive vaccine on the dynamics of HIV transmission

A. B. Gumel, S. M. Moghadas, R. E. Mickens

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

A deterministic mathematical model for the transmission dynamics of HIV infection in the presence of a preventive vaccine is considered. Although the equilibria of the model could not be expressed in closed form, their existence and threshold conditions for their stability are theoretically investigated. It is shown that the disease-free equilibrium is locally-asymptotically stable if the basic reproductive number ?<1 (thus, HIV disease can be eradicated from the community) and unstable if ?>1 (leading to the persistence of HIV within the community). A robust, positivity-preserving, non-standard finite-difference method is constructed and used to solve the model equations. In addition to showing that the anti-HIV vaccine coverage level and the vaccine-induced protection are critically important in reducing the threshold quantity ?, our study predicts the minimum threshold values of vaccine coverage and efficacy levels needed to eradicate HIV from the community.

Original languageEnglish (US)
Pages (from-to)649-659
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume9
Issue number6
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

Keywords

  • Basic reproductive number
  • Equilibria
  • Force of infection
  • Non-standard finite-difference schemes
  • Positivity property
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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