A Positivity-preserving Mickens-type Discretization of an Epidemic Model

S. M. Moghadas, M. E. Alexander, B. D. Corbett, A. B. Gumel

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.

Original languageEnglish (US)
Pages (from-to)1037-1051
Number of pages15
JournalJournal of Difference Equations and Applications
Volume9
Issue number11
DOIs
StatePublished - Nov 1 2003
Externally publishedYes

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Keywords

  • Basic reproductive number
  • Epidemic model
  • Mickens-type discretization
  • Preventive vaccine

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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