Global analysis of discrete-time SI and SIS epidemic models

Jianquan Li, Zhien Ma, Fred Brauer

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

Discrete-time SI and SIS models formulated as the discretization of a continuous-time model may exhibit behavior different from that of the continuous-time model such as period-doubling and chaotic behavior unless the step size in the model is sufficiently small. Some new discrete-time SI and SIS epidemic models with vital dynamics are formulated and analyzed. These new models do not exhibit period doubling and chaotic behavior and are thus better approximations to continuous models. However, their reproduction numbers and therefore their asymptotic behavior can differ somewhat from that of the corresponding continuous-time model.

Original languageEnglish (US)
Pages (from-to)699-710
Number of pages12
JournalMathematical Biosciences and Engineering
Volume4
Issue number4
DOIs
StatePublished - Oct 2007
Externally publishedYes

Keywords

  • Discrete-time epidemic model
  • Dynamic behavior
  • Equilibrium
  • Stability

ASJC Scopus subject areas

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

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