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.
Highlights
With the rapid growth of information technologies and network applications, severe challenges, in form of requirement of a suitable defense system, have been posed to make sure of the safety of the valuable information stored on system and in transit
(2) If condition (H3) is satisfied, the system will undergo Hopf bifurcation at the positive equilibrium E∗(S∗, I∗, D∗, Q∗, V∗) when τ = τk (k = 0, 1, 2, . . .), where τk is defined by (40). This implies that when time delay τ < τ0, the system will be stable at its infection equilibrium point so that it is easy to control and eliminate worms; when τ ≥ τ0, the system will be unstable but the threshold τ0 is greater than delayed model’s, which illustrates the model with constant quarantine strategy gets stable easier and the users have more time to remove worms
By considering that time delay leads to Hopf bifurcation so that the worm propagation system will be out of control, this paper proposes two quarantine strategies: constant
Summary
With the rapid growth of information technologies and network applications, severe challenges, in form of requirement of a suitable defense system, have been posed to make sure of the safety of the valuable information stored on system and in transit. Being infected by network worms or quarantined by IDS (intrusion detection systems), hosts will become dangerous and their owners will have to reinstall the system Another factor to consider is that when new computers are brought, most of them have preinstalled operating systems but without newest safety patches while old computers are discarded and recycled. Based on misuse intrusion detection system, we propose constant quarantine strategy It does improve vaccination effect, the system is still out of control and Hopf bifurcation is not eliminated either. This paper proposes a worm propagation model with impulsive quarantine strategy based on a hybrid intrusion detection system that combines both misuse and anomaly intrusion detection to make up for the gaps existing in the two systems.
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