Bifurcation analysis of a delayed SIS epidemic model with stage structure

This paper deals with a delayed SIS epidemic model with stage structure. The stability of the positive equilibrium and existence of Hopf bifurcation with delay τ is investigated. We show that the positive equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of positive equilibrium will cause a bifurcating periodic solution as the time delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument, we derive the explicit formulae for determining the direction of the bifurcation, the stability and other properties of the bifurcating periodic solutions. Analytic results are illustrated with numerical simulations.