The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model

Abdelhadi Abta, Hassan Laarabi and Hamad Talibi Alaoui

International Journal of Analysis, 2014, vol. 2014, 1-10

Abstract:

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 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.

Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/ANALYSIS/2014/940819.pdf (application/pdf)
http://downloads.hindawi.com/journals/ANALYSIS/2014/940819.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:ijanal:940819

DOI: 10.1155/2014/940819

Access Statistics for this article

More articles in International Journal of Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().