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Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease.
First of all, for any τ, we show that the disease-free equilibrium is globally asymptotically stable; when R0<1, the disease will die out.
Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for any τ=0; when R0>1, the disease will persist.
However, for any τ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained.
Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate.
At last, numerical simulations are performed to illustrate and verify the conclusions.
American Psychological Association (APA)
Xue, Yakui& Li, Tiantian. 2013. Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-507824
Modern Language Association (MLA)
Xue, Yakui& Li, Tiantian. Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth. Abstract and Applied Analysis No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-507824
American Medical Association (AMA)
Xue, Yakui& Li, Tiantian. Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-507824
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507824