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

被引：11

作者：

Abta, Abdelhadi ^{[1
]}

Laarabi, Hassan ^{[2
]}

Alaoui, Hamad Talibi ^{[3
]}

机构：

[1] Univ Cadi Ayyad, Fac Polydisciplinaire, Dept Math & Informat, Safi 4162, Morocco

[2] Univ Hassan II Mohammedia, Fac Sci Ben Msik, Dept Math & Informat, Casablanca 150, Morocco

[3] Univ Chouaib Doukkali, Fac Sci, Dept Math & Informat, El Jadida 20, Morocco

来源：

INTERNATIONAL JOURNAL OF ANALYSIS | 2014年

关键词：

D O I：

10.1155/2014/940819

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a delayed SIR model with saturated incidence rate. Thedelay is incorporated into the model in order to model the latent period. The basic reproductive number R-0 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 systemloses its stability and a Hopf bifurcation occurs. The model is extended to assess the impact of some control measures, by reformulating themodel 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.

引用

页数：10

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