Dynamical Analysis of SIR Epidemic Models with Distributed Delay
Joint Authors
Liu, Yulin
Chang, Zhengbo
Meng, Xinzhu
Zhao, Wencai
Zhang, Tongqian
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-22
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
SIR epidemic models with distributed delay are proposed.
Firstly, the dynamical behaviors of the model without vaccination are studied.
Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed.
The basic reproduction number R is got.
In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated.
And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem.
Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model.
The results can provide effective tactic basis for the practical infectious disease prevention.
American Psychological Association (APA)
Zhao, Wencai& Zhang, Tongqian& Chang, Zhengbo& Meng, Xinzhu& Liu, Yulin. 2013. Dynamical Analysis of SIR Epidemic Models with Distributed Delay. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-450158
Modern Language Association (MLA)
Zhao, Wencai…[et al.]. Dynamical Analysis of SIR Epidemic Models with Distributed Delay. Journal of Applied Mathematics No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-450158
American Medical Association (AMA)
Zhao, Wencai& Zhang, Tongqian& Chang, Zhengbo& Meng, Xinzhu& Liu, Yulin. Dynamical Analysis of SIR Epidemic Models with Distributed Delay. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-450158
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450158