Hopf bifurcation of a VEIQS worm propagation model in mobile networks with two delays

Abstract

The spread of worm virus has brought great loss to our production and life. In this paper, a new Vulnerable-Exposed-Infectious-Quarantined-Secured (VEIQS) worm propagation model with a saturated incidence and two delays is proposed. The local stability of the worm-existence equilibrium and the occurrence of Hopf bifurcation at the critical values of the two delays are obtained by regarding different combinations of time delays as bifurcation parameters. It shows that the model is ideal stable when the time delay is below the critical value and a Hopf bifurcation occurs when the time delay is above the critical value. In particular, direction and stability of the Hopf bifurcation are determined by using the center manifold theorem. Finally, some numerical simulations are presented in order to verify the analytical results.

Keywords

• Delay
• Bifurcation
• Delays
• Mobile networks
• Periodic solution
• VEIQS worm propagation model