中文摘要：

文章考虑了一类具有水平和垂直传播的离散传染病SIR模型的Flip分岔.文[1]利用系数参数确定了此类模型平衡点的双曲性,并通过非双曲的平衡点讨论其跨临界分岔性质.在文[1]的基础上,本文继续关注这类传染病模型的Flip分岔,通过导出描述中心流形的方程,讨论在无病平衡点的Flip分岔的方向和稳定性.

英文摘要：

In this article, the Flip bifurcation of a class of discrete deterministic SIR epidemic model with vertical and horizontal transmission is studied. In article [1], the hyperbolicity of equilibrium points is given by the coefficient parameters. And the transcritical bifurcation at the non--hyperbolic equilibrium point is discussed. In this article, we continue to study the Flip bifurcation of the class of the epidemic model. By getting the equation of center manifold, the direction and stability of the Flip bifurcation is dis- cussed.