Stability and Hopf bifurcation on an SEIR delayed model with logistic growth

Abstract

This paper investigates the stability and Hopf bifurcation of SEIR delay model with logistic growth. Firstly, the existence and uniqueness of equilibrium point are analyzed. For the study of the stability of the equilibrium point time delay (τ) was chosen as the bifurcation parameter. By considering the roots of characteristic equations, it was found that disease-free equilibrium is locally asymptotically stable for all τ ≥ 0 . The endemic equilibrium of the model is conditionally stable. Hopf bifurcation will occur when the bifurcation parameter passes through a critical value. Moreover, stability and direction of Hopf bifurcation are obtained by using the normal form theory and the center manifold reduction. Finally, the numerical solutions are simulated to verify the theoretical results.

Keywords

• SEIR model
• time delay
• logistic growth
• local stability
• Hopf bifurcation