Stability of the endemic equilibrium in epidemic models with subpopulations

Herbert W. Hethcote, Horst R. Thieme

Research output: Contribution to journalArticlepeer-review

131 Scopus citations


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
Issue number2
StatePublished - Aug 1985
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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