An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

A. B. Gumel, C. Connell Mccluskey, James Watmough

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If R v ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv > 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming Ho = 4). Numerical simulations are used to explore the severity of outbreaks when R v > 1.

Original languageEnglish (US)
Pages (from-to)485-512
Number of pages28
JournalMathematical Biosciences and Engineering
Volume3
Issue number3
DOIs
StatePublished - Jul 2006
Externally publishedYes

Keywords

  • Control reproduction number
  • Disease transmission model
  • Epidemiology
  • Severe acute respiratory syndrome (SARS)
  • Vaccination

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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