Bifurcations and chaos in a discrete SI epidemic model with fractional order

Abstract

In this study, a new discrete SI epidemic model is proposed and established from SI fractional-order epidemic model. The existence conditions, the stability of the equilibrium points and the occurrence of bifurcation are analyzed. By using the center manifold theorem and bifurcation theory, it is shown that the model undergoes flip and Neimark–Sacker bifurcation. The effects of step size and fractional-order parameters on the dynamics of the model are studied. The bifurcation analysis is also conducted and our numerical results are in agreement with theoretical results.