Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function
Joint Authors
Zhang, Weipeng
Deng, Guifeng
Xiao, Yanju
Liu, Zhehua
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-01-19
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function.
The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger.
Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper.
The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical.
By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived.
Finally, mathematical analysis and numerical simulations are given to support our theoretical results.
American Psychological Association (APA)
Xiao, Yanju& Zhang, Weipeng& Deng, Guifeng& Liu, Zhehua. 2015. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1074634
Modern Language Association (MLA)
Xiao, Yanju…[et al.]. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function. Mathematical Problems in Engineering No. 2015 (2015), pp.1-14.
https://search.emarefa.net/detail/BIM-1074634
American Medical Association (AMA)
Xiao, Yanju& Zhang, Weipeng& Deng, Guifeng& Liu, Zhehua. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1074634
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074634