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 | |
| State | Published - Mar 15 2004 |
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Keywords
- Bifurcation
- Constant removal rate
- Epidemic
- Global analysis
- Limit cycle
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Bifurcations in an epidemic model with constant removal rate of the infectives. / Wang, Wendi; Ruan, Shigui.
In: Journal of Mathematical Analysis and Applications, Vol. 291, No. 2, 15.03.2004, p. 775-793.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bifurcations in an epidemic model with constant removal rate of the infectives
AU - Wang, Wendi
AU - Ruan, Shigui
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
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 -