On periodic solutions of a delay integral equation modelling epidemics

H. L. Smith

Research output: Contribution to journalArticle

36 Scopus citations

Abstract

A delay-integral equation, proposed by Cooke and Kaplan in [1] as a model of epidemics, is studied. The focus of this work is on the qualitative behavior of solutions as a certain parameter is allowed to vary. It is shown that if a certain threshold is not exceeded then solutions tend to zero exponentially while if this threshold is exceeded, periodic solutions exist. Many features of the numerical studies in [1] are explained.

Original languageEnglish (US)
Pages (from-to)69-80
Number of pages12
JournalJournal Of Mathematical Biology
Volume4
Issue number1
DOIs
StatePublished - Mar 1977
Externally publishedYes

ASJC Scopus subject areas

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

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