![](/images/graphics-bg.png)
Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-08-30
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
A delayed epidemic model with nonlinear incidence rate which depends on the ratio of the numbers of susceptible and infectious individuals is considered.
By analyzing the corresponding characteristic equations, the effects of time delay on the stability of the equilibria are studied.
By choosing time delay as bifurcation parameter, the critical value of time delay at which a Hopf bifurcation occurs is obtained.
In order to derive the normal form of the Hopf bifurcation, an extended method of multiple scales is developed and used.
Then, the amplitude of bifurcating periodic solution and the conditions which determine the stability of the bifurcating periodic solution are obtained.
The validity of analytical results is shown by their consistency with numerical simulations.
American Psychological Association (APA)
Wang, Wanyong& Chen, Lijuan. 2016. Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1111832
Modern Language Association (MLA)
Wang, Wanyong& Chen, Lijuan. Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales. Mathematical Problems in Engineering No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1111832
American Medical Association (AMA)
Wang, Wanyong& Chen, Lijuan. Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1111832
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1111832