Models for transmission of disease with immigration of infectives

Fred Brauer, P. Van Den Driessche

Research output: Contribution to journalArticlepeer-review

176 Scopus citations


Simple models for disease transmission that include immigration of infective individuals and variable population size are constructed and analyzed. A model with a general contact rate for a disease that confers no immunity admits a unique endemic equilibrium that is globally stable. A model with mass action incidence for a disease in which infectives either die or recover with permanent immunity has the same qualitative behavior. This latter result is proved by reducing the system to an integro-differential equation. If mass action incidence is replaced by a general contact rate, then the same result is proved locally for a disease that causes fatalities. Threshold-like results are given, but in the presence of immigration of infectives there is no disease-free equilibrium. A considerable reduction of infectives is suggested by the incorporation of screening and quarantining of infectives in a model for HIV transmission in a prison system.

Original languageEnglish (US)
Pages (from-to)143-154
Number of pages12
JournalMathematical Biosciences
Issue number2
StatePublished - 2001
Externally publishedYes


  • Epidemic model
  • Global stability
  • Immigration
  • Quarantine
  • Threshold

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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