DYNAMICAL ASPECTS OF A DELAYED COMPUTER VIRUSES MODEL WITH HORIZONTAL AND VERTICAL DISSEMINATION OVER INTERNET

Abstract

In this paper, to explore propagation dynamics of computer viruses over the Internet, a delayed SLBRS (susceptible–latent–breaking-out–recovering–susceptible) model of computer viruses considering horizontal and vertical dissemination over Internet is studied. The basic reproduction number at which computer viruses are prone to be extinct or continue to exist is calculated with the help of the next generation matrix method. By choosing the time delay because of processing time consumed to recover the breaking-out computers as bifurcation parameter, a series of sufficient criteria for experience of Hopf bifurcation are derived. Specially, optimal strategies to control dissemination of computer viruses over Internet are established. Finally, numerical simulations for certificating correctness of our theoretical findings are carried out. The findings show that the exhibition of Hopf bifurcation has an important impact on prediction and control of the propagation of computer viruses over the Internet.