Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy

Abstract

Internet worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to Internet in the real world. To begin with, a worm propagation model with time delay in vaccination is formulated. Through theoretical analysis, it is proved that the worm propagation system is stable when the time delay is less than the thresholdτ0and Hopf bifurcation appears when time delay is equal to or greater thanτ0. Then, a worm propagation model with constant quarantine strategy is proposed. Through quantitative analysis, it is found that constant quarantine strategy has some inhibition effect but does not eliminate bifurcation. Considering all the above, we put forward impulsive quarantine strategy to eliminate worms. Theoretical results imply that the novel proposed strategy can eliminate bifurcation and control the stability of worm propagation. Finally, simulation results match numerical experiments well, which fully supports our analysis.

An Epidemic Model of Computer Worms with Time Delay and Variable Infection Rate

“…Some research achievements [10][11][12] showed that the spread dynamic system of malware would be unstable and bifurcation and chaos would appear. Considering the fact that the intrusion detection system (IDS) may lead to time delay, Yao et al [13][14][15] obtained the threshold of time delay when Hopf bifurcation occurred. Pulse quarantine strategy [16] also has been taken to constrain the propagation of worms in network.…”

On the Optimal Dynamic Control Strategy of Disruptive Computer Virus

“…First, the bandwidth resources consumed in the virus control process should be measured and incorporated in the cost. Second, the optimal dynamic control problem should be investigated under sophisticated epidemic models such as the impulsive epidemic models [51,52], the stochastic epidemic models [53][54][55], and the epidemic models on time-varying networks [56][57][58]. Last, it is rewarding to apply the methodology developed in this paper to the optimal dynamic control of rumor spreading [59][60][61].…”

Hopf bifurcation analysis for an epidemic model over the Internet with two delays

“…Considering the fact that the recovered computers may be infected again after a temporary immunity period, Zhang and Yang [19] proposed a computer virus model with two delays based on the work in [18] and studied the Hopf bifurcation by regarding the possible combinations of the two delays as a bifurcation parameter. In addition, many researchers introduced the quarantine strategy into mathematical models and investigated the Hopf bifurcation of the models in order to describe dynamics of computer viruses in a network [20][21][22][23]. Recently, Zhang and Wang [24] proposed the following SLBQRS (Susceptible-Latent-Breaking-Quarantined-Recovered-Susceptible) computer virus model with latent and breaking-out over the Internet:…”