Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission


Authors

Wenju Du - School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China. Jiangang Zhang - Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China. Shuang Qin - Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China. Jianning Yu - School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.


Abstract

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.


Keywords


MSC


References