On periodic solutions of a delay integral equation modelling epidemics

Research output: Contribution to journalArticle

36 Citations (Scopus)

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

Fingerprint

Delay Equations
Integral equations
Periodic Solution
Integral Equations
Qualitative Behavior
Behavior of Solutions
Modeling
Numerical Study
Vary
Tend
Zero
Model

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

Cite this

On periodic solutions of a delay integral equation modelling epidemics. / Smith, Hal.

In: Journal of Mathematical Biology, Vol. 4, No. 1, 03.1977, p. 69-80.

Research output: Contribution to journalArticle

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