Bifurcations in an epidemic model with constant removal rate of the infectives

Wendi Wang; Shigui Ruan

doi:10.1016/j.jmaa.2003.11.043

Bifurcations in an epidemic model with constant removal rate of the infectives

Wendi Wang, Shigui Ruan

Mathematics

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

147 Scopus citations

Abstract

An epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation, and homoclinic bifurcation.

Original language	English (US)
Pages (from-to)	775-793
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	291
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2003.11.043
State	Published - Mar 15 2004

Keywords

Bifurcation
Constant removal rate
Epidemic
Global analysis
Limit cycle

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2003.11.043

Fingerprint Dive into the research topics of 'Bifurcations in an epidemic model with constant removal rate of the infectives'. Together they form a unique fingerprint.

Cite this

@article{b9073d76f980423a8ea5d85b76310910,

title = "Bifurcations in an epidemic model with constant removal rate of the infectives",

abstract = "An epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation, and homoclinic bifurcation.",

keywords = "Bifurcation, Constant removal rate, Epidemic, Global analysis, Limit cycle",

author = "Wendi Wang and Shigui Ruan",

note = "Funding Information: * Corresponding author. E-mail address: ruan@math.miami.edu (S. Ruan). 1 Research was supported by the Key Teachers Fund from the Minister of Education of China and the National Natural Science Fund of China. 2 Research was partially supported by the NSERC of Canada and by a start-up fund from the College of Arts and Sciences at the University of Miami. On leave from Dalhousie University, Halifax, Canada.",

year = "2004",

month = mar,

day = "15",

doi = "10.1016/j.jmaa.2003.11.043",

language = "English (US)",

volume = "291",

pages = "775--793",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Bifurcations in an epidemic model with constant removal rate of the infectives

AU - Wang, Wendi

AU - Ruan, Shigui

N1 - Funding Information: * Corresponding author. E-mail address: ruan@math.miami.edu (S. Ruan). 1 Research was supported by the Key Teachers Fund from the Minister of Education of China and the National Natural Science Fund of China. 2 Research was partially supported by the NSERC of Canada and by a start-up fund from the College of Arts and Sciences at the University of Miami. On leave from Dalhousie University, Halifax, Canada.

PY - 2004/3/15

Y1 - 2004/3/15

N2 - An epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation, and homoclinic bifurcation.

AB - An epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infectives on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation, and homoclinic bifurcation.

KW - Bifurcation

KW - Constant removal rate

KW - Epidemic

KW - Global analysis

KW - Limit cycle

UR - http://www.scopus.com/inward/record.url?scp=1542406443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542406443&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2003.11.043

DO - 10.1016/j.jmaa.2003.11.043

M3 - Article

AN - SCOPUS:1542406443

VL - 291

SP - 775

EP - 793

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -