Bifurcation analysis on a delayed SIS epidemic model with stage structure

Abstract

In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.

Keywords

• SIS model
• delay
• Hopf bifurcation
• stability
• periodic solution