Backward bifurcations in simple vaccination/treatment models

Fred Brauer

doi:10.1080/17513758.2010.510584

Backward bifurcations in simple vaccination/treatment models

Fred Brauer

CLAS-NS: Mathematical Computational Modeling Sciences Center, Simon A. Levin (MCMSC)

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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 language	English (US)
Pages (from-to)	410-418
Number of pages	9
Journal	Journal of biological dynamics
Volume	5
Issue number	5
DOIs	https://doi.org/10.1080/17513758.2010.510584
State	Published - Sep 2011

Keywords

Backward bifurcation
Temporary immunity
Treatment
Vaccination

ASJC Scopus subject areas

Ecology, Evolution, Behavior and Systematics
Ecology

Access to Document

10.1080/17513758.2010.510584

Fingerprint Dive into the research topics of 'Backward bifurcations in simple vaccination/treatment models'. Together they form a unique fingerprint.

Cite this

@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",

note = "Funding Information: The exposition of backward bifurcations and multiple endemic equilibria has been improved substantially by the suggestion of an anonymous reviewer. This research was supported by NSERC Research Grant OGPIN #203901-99.",

year = "2011",

month = sep,

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

N1 - Funding Information: The exposition of backward bifurcations and multiple endemic equilibria has been improved substantially by the suggestion of an anonymous reviewer. This research was supported by NSERC Research Grant OGPIN #203901-99.

PY - 2011/9

Y1 - 2011/9

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

AN - SCOPUS:84860392829

VL - 5

SP - 410

EP - 418

JO - Journal of Biological Dynamics

JF - Journal of Biological Dynamics

SN - 1751-3758

IS - 5

ER -

Backward bifurcations in simple vaccination/treatment models

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this