一类具有临时免疫的时滞蠕虫传播模型的Hopf分支(Delay induced Hopf bifurcation in a worm propagation model with partial immunization)

Abstract

This paper is devoted to Hopf bifurcation of a delayed SVEIR model with partial immunization that describes worms propagation on internet. Sufficient conditions for existence of Hopf bifurcation are obtained by considering the latent period time delay of worms as the bifurcation parameter. Properties of Hopf bifurcation are then investigated with the help of the normal form theory and the center manifold theorem. Numerical simulations show that worms propagation in internet can be controlled and eliminated by shortening the time delay.

Keywords

• sveir model
• hopf bifurcation
• time delay
• stability
• periodic solutions