Hopf Bifurcation in an SEIDQV Worm Propagation Model with Quarantine Strategy

Security and Communication Networks

et al. 2018

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With rapid development of Internet, network security issues become increasingly serious. Temporary patches have been put on the infectious hosts, which may lose efficacy on occasions. This leads to a time delay when vaccinated hosts change to susceptible hosts. On the other hand, the worm infection is usually a nonlinear process. Considering the actual situation, a variable infection rate is introduced to describe the spread process of worms. According to above aspects, we propose a time-delayed worm propagation model with variable infection rate. Then the existence condition and the stability of the positive equilibrium are derived. Due to the existence of time delay, the worm propagation system may be unstable and out of control. Moreover, the threshold 0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than 0 . When time delay is over 0 , the system will be unstable. In addition, numerical experiments have been performed, which can match the conclusions we deduce. The numerical experiments also show that there exists a threshold in the parameter , which implies that we should choose appropriate infection rate ( ) to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions.

“…If = 0 , then ± 0 is a pair of purely imaginary roots of (12). Moreover, if the conditions in Lemma 3.4 (1) in [14] are satisfied, then…”

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Yao

Security and Communication Networks

et al. 2018

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“…As far as we know, the use of quarantine strategies has produced a great effect on controlling disease. People use quarantine strategies widely in worm containment enlightened by this [10][11][12][13][14][15][16]. In addition, some scholars have done research on time delay [17][18][19].…”

Section: Related Workmentioning

confidence: 99%

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

Yao

Feng

Mathematical Problems in Engineering

et al. 2014

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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.

“…Yao et al research the worm propagation model by considering the time delay [28]. They found that time delay may lead to Hopf bifurcation phenomenon which will make the worm propagation system unstable and uncontrollable.…”

Section: Related Workmentioning

confidence: 99%

Modeling the Propagation of Mobile Phone Virus under Complex Network

The Scientific World Journal

Wei

Guo³

et al. 2014

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Mobile phone virus is a rogue program written to propagate from one phone to another, which can take control of a mobile device by exploiting its vulnerabilities. In this paper the propagation model of mobile phone virus is tackled to understand how particular factors can affect its propagation and design effective containment strategies to suppress mobile phone virus. Two different propagation models of mobile phone viruses under the complex network are proposed in this paper. One is intended to describe the propagation of user-tricking virus, and the other is to describe the propagation of the vulnerability-exploiting virus. Based on the traditional epidemic models, the characteristics of mobile phone viruses and the network topology structure are incorporated into our models. A detailed analysis is conducted to analyze the propagation models. Through analysis, the stable infection-free equilibrium point and the stability condition are derived. Finally, considering the network topology, the numerical and simulation experiments are carried out. Results indicate that both models are correct and suitable for describing the spread of two different mobile phone viruses, respectively.