Neimark-Sacker bifurcation and control of a discrete epidemic model

In this paper, a discrete epidemic model with nonlinear incidence rate obtained by the forward Euler method is investigated. The conditions of existence for Neimark-Sacker bifurcation are derived by using bifurcation theory. In order to eliminate the Neimark-Sacker bifurcation of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations illustrate the validity of the proposed results.