Stability of the endemic equilibrium in epidemic models with subpopulations

Herbert W. Hethcote, Horst Thieme

Research output: Contribution to journalArticle

94 Citations (Scopus)

Abstract

For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.

Original languageEnglish (US)
Pages (from-to)205-227
Number of pages23
JournalMathematical Biosciences
Volume75
Issue number2
DOIs
StatePublished - 1985
Externally publishedYes

Fingerprint

Endemic Equilibrium
Epidemic Model
subpopulation
Communicable Diseases
Immunity
Immunization
Infection
Population
immunization
Integrodifferential equations
infectivity
Infectious Diseases
infectious disease
immunity
Asymptotically Stable
age class
System of Ordinary Differential Equations
Ordinary differential equations
Integro-differential Equation
infectious diseases

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Stability of the endemic equilibrium in epidemic models with subpopulations. / Hethcote, Herbert W.; Thieme, Horst.

In: Mathematical Biosciences, Vol. 75, No. 2, 1985, p. 205-227.

Research output: Contribution to journalArticle

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