Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination

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. (c) 2020 Elsevier Ltd. All rights reserved.