Geodesic
Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission
Du, Wenju1 ; Zhang, Jiangang2 ; Qin, Shuang2 ; Yu, Jianning1
1 School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China
2 Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 4976-4989.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The aim of paper is dealing with the dynamical behaviors of a discrete SIR epidemic model with the saturated contact rate and vertical transmission. More precisely, we investigate the local stability of equilibriums, the existence, stability and direction of flip bifurcation and Neimark-Sacker bifurcation of the model by using the center manifold theory and normal form method. Finally, the numerical simulations are provided for justifying the validity of the theoretical analysis.
DOI : 10.22436/jnsa.009.07.02
Classification : 92D30, 37N25, 39A28
Keywords: Discrete SIR epidemic model, stability, flip bifurcation, Neimark-Sacker bifurcation.

Du, Wenju 1 ; Zhang, Jiangang 2 ; Qin, Shuang 2 ; Yu, Jianning 1

1 School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China
2 Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China 
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Du, Wenju; Zhang, Jiangang; Qin, Shuang; Yu, Jianning. Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 4976-4989. doi : 10.22436/jnsa.009.07.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.07.02/

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