Dynamics of an epidemic model with delays and stage structure

In this paper, dynamics of a stage-structured epidemic model with delays and nonlinear incidence rate is analyzed. Local stability and existence of Hopf bifurcation is discussed by choosing possible combination of the delays as the bifurcation parameter. It is proved that the unique endemic equilibrium is locally asymptotically stable when the delay is suitably small and a bifurcating periodic solution will be caused once the delay passes through the corresponding critical value of the delay. We make use of the normal form theory and center manifold theorem to obtain the explicit formulas for determining the properties of the Hopf bifurcation. Numerical simulations supporting our obtained findings are carried out in the end.