Backward bifurcations in simple vaccination/treatment models

Fred Brauer

Research output: Contribution to journal › Article

13 Citations (Scopus)

Abstract

We describe and analyse by elementary means some simple models for disease transmission with vaccination and treatment. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. The results are applicable to epidemic models in which demographic effects are ignored, but there is temporary immunity following recovery from infection.

Original languageEnglish (US)
Pages (from-to)410-418
Number of pages9
JournalJournal of Biological Dynamics
Volume5
Issue number5
DOIs
StatePublished - Sep 1 2011
Externally publishedYes

Fingerprint

vaccination
bifurcation
disease transmission
immunity
demographic statistics
infection
effect

Keywords

  • Backward bifurcation
  • Temporary immunity
  • Treatment
  • Vaccination

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

Cite this

Backward bifurcations in simple vaccination/treatment models. / Brauer, Fred.

In: Journal of Biological Dynamics, Vol. 5, No. 5, 01.09.2011, p. 410-418.

Research output: Contribution to journal › Article

Brauer, F 2011, 'Backward bifurcations in simple vaccination/treatment models', Journal of Biological Dynamics, vol. 5, no. 5, pp. 410-418. https://doi.org/10.1080/17513758.2010.510584
Brauer F. Backward bifurcations in simple vaccination/treatment models. Journal of Biological Dynamics. 2011 Sep 1;5(5):410-418. https://doi.org/10.1080/17513758.2010.510584
Brauer, Fred. / Backward bifurcations in simple vaccination/treatment models. In: Journal of Biological Dynamics. 2011 ; Vol. 5, No. 5. pp. 410-418.
@article{b6a2a36f0d2d4c2db43d43952a3bcaa1,
title = "Backward bifurcations in simple vaccination/treatment models",
abstract = "We describe and analyse by elementary means some simple models for disease transmission with vaccination and treatment. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. The results are applicable to epidemic models in which demographic effects are ignored, but there is temporary immunity following recovery from infection.",
keywords = "Backward bifurcation, Temporary immunity, Treatment, Vaccination",
author = "Fred Brauer",
year = "2011",
month = "9",
day = "1",
doi = "10.1080/17513758.2010.510584",
language = "English (US)",
volume = "5",
pages = "410--418",
journal = "Journal of Biological Dynamics",
issn = "1751-3758",
publisher = "Taylor and Francis Ltd.",
number = "5",

}

TY - JOUR

T1 - Backward bifurcations in simple vaccination/treatment models

AU - Brauer, Fred

PY - 2011/9/1

Y1 - 2011/9/1

N2 - We describe and analyse by elementary means some simple models for disease transmission with vaccination and treatment. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. The results are applicable to epidemic models in which demographic effects are ignored, but there is temporary immunity following recovery from infection.

AB - We describe and analyse by elementary means some simple models for disease transmission with vaccination and treatment. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. The results are applicable to epidemic models in which demographic effects are ignored, but there is temporary immunity following recovery from infection.

KW - Backward bifurcation

KW - Temporary immunity

KW - Treatment

KW - Vaccination

UR - http://www.scopus.com/inward/record.url?scp=84860392829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860392829&partnerID=8YFLogxK

U2 - 10.1080/17513758.2010.510584

DO - 10.1080/17513758.2010.510584

M3 - Article

VL - 5

SP - 410

EP - 418

JO - Journal of Biological Dynamics

JF - Journal of Biological Dynamics

SN - 1751-3758

IS - 5

ER -

Access to Document