In this paper, a discrete-time SEIR measles epidemic model with fractional-order and constant vaccination is investigated. The basic reproduction number with an algebraic criterion are used to study the local asymptotic stability of the equilibrium points. Two types of codimension one bifurcation namely, flip and Neimark-Sacker (N-S) bifurcations and their intersection codimension two flip-N-S bifurcation, are discussed. The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. The criterions employed are based on the coefficients of characteristic equations rather than the properties of eigenvalues of Jacobian matrix. The output is a semi-algebraic system composed of a set of equations, inequalities and inequations. These criterions represent appropriate conditions for codim-1 and codim-2 bifurcations of high dimensional maps.

本文研究了具有分数阶和恒定疫苗接种的离散时间SEIR麻疹流行模型。使用带有代数准则的基本再生产数来研究平衡点的局部渐近稳定性。讨论了两种类型的共维一分叉，即翻转和Neimark-Sacker（NS）分叉，以及它们的相交维数两个翻转NS分叉。使用代数准则方法得出用于检测这些类型的分叉的充要条件。所采用的准则是基于特征方程的系数，而不是基于雅可比矩阵特征值的性质。输出是由一组方程，不等式和不等式组成的半代数系统。