Models for transmission of disease with immigration of infectives

Fred Brauer, P. Van Den Driessche

Research output: Contribution to journalReview article

144 Citations (Scopus)

Abstract

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
Volume171
Issue number2
DOIs
StatePublished - Jul 4 2001
Externally publishedYes

Fingerprint

Immigration
Emigration and Immigration
disease transmission
immigration
immunity
Immunity
correctional institutions
Incidence
Contact
Prisons
human immunodeficiency virus
Model
disease incidence
Endemic Equilibrium
Integrodifferential equations
Qualitative Behavior
population size
Population Density
Population Size
Integro-differential Equation

Keywords

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

ASJC Scopus subject areas

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

Cite this

Models for transmission of disease with immigration of infectives. / Brauer, Fred; Van Den Driessche, P.

In: Mathematical Biosciences, Vol. 171, No. 2, 04.07.2001, p. 143-154.

Research output: Contribution to journalReview article

Brauer, Fred ; Van Den Driessche, P. / Models for transmission of disease with immigration of infectives. In: Mathematical Biosciences. 2001 ; Vol. 171, No. 2. pp. 143-154.
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