Bifurcation analysis of a delayed SIS epidemic model with stage structure

This paper deals with it delayed SIS epidemic model with stage structure. The stability of the positive equilibrium and existence of Hopf bifurcation with delay tau is investigated. We show that the positive equilibrium is locally asymptotically stable when the time May is Small enough, while change of stability of positive equilibrium will cause a bifurcating,the periodic solution as the time delay tau passess through it 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. (C) 2007 Elsevier Ltd. All rights reserved.