Bifurcation analysis of an SIS epidemic model with nonlinear birth rate

This paper deals with an SIS epidemic model with delay. By regarding p as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. The explicit formulae determining the direction of the bifurcations, the stability and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. Some numerical simulations are also included.