The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model
Joint Authors
Abta, Abdelhadi
Talibi Alaoui, Hamad
Laarabi, Hassan
Source
International Journal of Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-07
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We propose a delayed SIR model with saturated incidence rate.
The delay is incorporated into the model in order to model the latent period.
The basic reproductive number R0 is obtained.
Furthermore, using time delay as a bifurcation parameter, it is proven that there exists a critical value of delay for the stability of diseases prevalence.
When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs.
The model is extended to assess the impact of some control measures, by reformulating the model as an optimal control problem with vaccination and treatment.
The existence of the optimal control is also proved.
Finally, some numerical simulations are performed to verify the theoretical analysis.
American Psychological Association (APA)
Abta, Abdelhadi& Laarabi, Hassan& Talibi Alaoui, Hamad. 2014. The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model. International Journal of Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-509951
Modern Language Association (MLA)
Abta, Abdelhadi…[et al.]. The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model. International Journal of Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-509951
American Medical Association (AMA)
Abta, Abdelhadi& Laarabi, Hassan& Talibi Alaoui, Hamad. The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model. International Journal of Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-509951
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509951