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

Abba Gumel, C. Connell Mccluskey, James Watmough

Research output: Contribution to journalArticle

45 Citations (Scopus)

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
StatePublished - Jul 2006
Externally publishedYes

Fingerprint

Severe Acute Respiratory Syndrome
Vaccines
Vaccine
Imperfect
vaccines
Efficacy
Disease Outbreaks
Compound Matrices
burden of disease
Vaccine Efficacy
Model
Quarantine
Reproduction number
Lyapunov functions
quarantine
dynamic models
Deterministic Model
Virus Diseases
clinical trials
mathematical models

Keywords

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

ASJC Scopus subject areas

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

Cite this

An sveir model for assessing potential impact of an imperfect anti-SARS vaccine. / Gumel, Abba; Connell Mccluskey, C.; Watmough, James.

In: Mathematical Biosciences and Engineering, Vol. 3, No. 3, 07.2006, p. 485-512.

Research output: Contribution to journalArticle

Gumel, Abba ; Connell Mccluskey, C. ; Watmough, James. / An sveir model for assessing potential impact of an imperfect anti-SARS vaccine. In: Mathematical Biosciences and Engineering. 2006 ; Vol. 3, No. 3. pp. 485-512.
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