Global stability of a generalized epidemic model

Shingo Iwami, Tadayuki Hara

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable - the global result has not been established previously.

Original languageEnglish
Pages (from-to)286-300
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume362
Issue number2
DOIs
Publication statusPublished - Feb 15 2010
Externally publishedYes

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Epidemiology
Epidemic Model
System theory
Lyapunov functions
Global Stability
Dynamical systems
Competitive Exclusion
Basic Reproductive number
Globally Asymptotically Stable
Systems Theory
Lyapunov Function
Biology
Dynamical system
Theorem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Global stability of a generalized epidemic model. / Iwami, Shingo; Hara, Tadayuki.

In: Journal of Mathematical Analysis and Applications, Vol. 362, No. 2, 15.02.2010, p. 286-300.

Research output: Contribution to journalArticle

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