Hopf bifurcation analysis for an SIRS epidemic model with logistic growth and delays

A delayed SIRS epidemic model with logistic growth is investigated in this paper. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combination of the two delays as a bifurcation parameter and analyzing distribution of roots of the corresponding characteristic equations. Particularly, the direction and stability of the local Hopf bifurcation are determined by using the normal form theory and center manifold theorem. Finally, some numerical simulations are provided in order to illustrate the theoretical results. © 2015, Korean Society for Computational and Applied Mathematics.