Delay-induced Hopf bifurcation of an SVEIR computer virus model with nonlinear incidence rate

Abstract

We are concerned with the Hopf bifurcation of an SVEIR computer virus model with time delay and nonlinear incident rate. First of all, by analyzing the associated characteristic equation we obtain sufficient conditions for its local stability and the existence of a Hopf bifurcation. Directly afterward, by means of the normal form theory and the center manifold theorem we derive explicit formulas that determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions. Finally, we carry out numerical simulations to illustrate and verify the theoretical results.