Dynamics analysis of a new fractional-order SVEIR-KS model for computer virus propagation: Stability and Hopf bifurcation

This work investigates the stability and Hopf bifurcation of a fractional -order model of the computer virus known as Susceptible-Vaccinated-Exposed-Infected-Recovered-Kill Signals (SVEIR-KS) that has two delays. Utilizing the linearization technique, Laplace transform, Routh-Hurwitz criteria, and Hopf bifurcation theorem of fractional -order differential systems, the sufficient criteria for the system's stability and Hopf bifurcation are determined. The study demonstrates that the stability and occurrence of the Hopf bifurcation of the fractional -order computer virus model are profoundly affected by fractional order q and time delays. In order to confirm the validity of the theoretical results, various simulations and examples with appropriate parameters are provided. The results show a negative correlation between the delay critical value and the fractional order q. Additionally we also dig into the effect in which kill signals prevent computer viruses from spreading over a network.