Periodic solutions: A robust numerical method for an S-I-R model of epidemics

F. A. Milner, A. Pugliese

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic, just as suggested by the instability of the endemic steady state.

Original languageEnglish (US)
Pages (from-to)471-492
Number of pages22
JournalJournal Of Mathematical Biology
Volume39
Issue number6
DOIs
StatePublished - Dec 1999
Externally publishedYes

Keywords

  • Epidemic model
  • Instability of equilibrium
  • Numerical methods
  • Periodic solutions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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