摘要：In this paper, we are concerned with the theoretical analysis of the bifurcations for a deterministic SIR epidemic model in discrete time. By deriving equations describing flows on the center manifolds, we discuss the transcritical bifurcation at the disease-free equilibrium point and the direction and stability of the flip bifurcation at the positive endemic equilibrium point. We give explicit conditions to check the stability of equilibrium points and the critical parameter for the emergence of a flip bifurcation. For illustrating the theoretical analysis, we also give some numerical simulation examples. MSC:37N25, 39A11, 92B05.
关键词：center manifold ; discrete time ; epidemic model ; flip bifurcation ; transcritical bifurcation
