Analysis of an internet worm propagation model with graded infection rates

2013 ◽  
Author(s):  
Fangwei Wang ◽  
Yunkai Zhang ◽  
Honggang Guo ◽  
Jianfeng Ma
Keyword(s):  
Propagation Model ◽  
Infection Rates ◽  
Worm Propagation ◽  
Internet Worm

scholarly journals The Influence of User Protection Behaviors on the Control of Internet Worm Propagation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yihong Li ◽  
Jinxiao Pan ◽  
Lipeng Song ◽  
Zhen Jin
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Propagation Model ◽  
Sis Model ◽  
Worm Propagation ◽  
Internet Worm ◽  
User Behaviors ◽  
New Findings ◽  
And Control ◽  
User Protection

Computer users’ reactions to the outbreak of Internet worm directly determine the defense capability of the computer and play an important role in the spread of worm. In this paper, in order to characterize the impacts of adaptive user protection behaviors, an improved SIS model is proposed to describe the Internet worm propagation. The results of theoretical analysis indicate that the protective campaigns of users can indeed reduce the worm’s reproduction number to values less than one. But it may not be sufficient to eradicate the worm. In certain condition, a backward bifurcation leading to bistability can occur. These are new findings in the worm propagation model that bring new challenges to control the spread of the worm and further demonstrate the importance of user behaviors in controlling the worm propagation. Corresponding to the analysis results, defense and control strategies are provided.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Yao ◽  
Xiaodong Feng ◽  
Wei Yang ◽  
Wenlong Xiang ◽  
Fuxiang Gao
Keyword(s):  
Time Delay ◽  
Propagation Model ◽  
The Novel ◽  
Worm Propagation ◽  
Internet Worm ◽  
Internet Worms ◽  
The Stability ◽  
And Control ◽  
Theoretical Results ◽  
Significant Attention

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.

scholarly journals Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Yao ◽  
Nan Zhang ◽  
Wenlong Xiang ◽  
Ge Yu ◽  
Fuxiang Gao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Simulation Experiments ◽  
Death Rates ◽  
Worm Propagation ◽  
Modeling And Analysis ◽  
Internet Worm ◽  
The Stability

A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical valueτ0of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less thanτ0. However, Hopf bifurcation appears when time delayτpasses the thresholdτ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less thanτ0to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis.

scholarly journals Hopf bifurcation in an Internet worm propagation model with time delay in quarantine

2013 ◽  
Vol 57 (11-12) ◽  
pp. 2635-2646 ◽  
Author(s):  
Yu Yao ◽  
Xiao-wu Xie ◽  
Hao Guo ◽  
Ge Yu ◽  
Fu-Xiang Gao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Propagation Model ◽  
Worm Propagation ◽  
Internet Worm

scholarly journals Internet Worm Propagation Model Using Centrality Theory

2016 ◽  
Vol 56 (4) ◽  
pp. 1191-1205 ◽  
Author(s):  
Su-Kyung Kwon ◽  
Yoon-Ho Choi ◽  
Hunki Baek
Keyword(s):  
Propagation Model ◽  
Worm Propagation ◽  
Internet Worm

Pulse quarantine strategy of internet worm propagation: Modeling and analysis

2012 ◽  
Vol 38 (5) ◽  
pp. 1047-1061 ◽  
Author(s):  
Yu Yao ◽  
Lei Guo ◽  
Hao Guo ◽  
Ge Yu ◽  
Fu-xiang Gao ◽  
...  
Keyword(s):  
Worm Propagation ◽  
Modeling And Analysis ◽  
Internet Worm ◽  
Propagation Modeling

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

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Yao ◽  
Qiang Fu ◽  
Wei Yang ◽  
Ying Wang ◽  
Chuan Sheng
Keyword(s):  
Time Delay ◽  
Infection Rate ◽  
Numerical Experiments ◽  
Rapid Development ◽  
Nonlinear Process ◽  
Existence Condition ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Worm Propagation ◽  
Security Issues

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 τ0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than τ0. When time delay is over τ0, 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 a, which implies that we should choose appropriate infection rate β(t) to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions.

scholarly journals Impulsive Switching Epidemic Model with Benign Worm Defense and Quarantine Strategy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Jiying Lai ◽  
Shujing Gao ◽  
Yujiang Liu ◽  
Xinzhu Meng
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Propagation Model ◽  
The Internet ◽  
Worm Propagation ◽  
Worm Defense ◽  
Benign Worm ◽  
Significant Attention

The issue on how to effectively control Internet malicious worms has been drawn significant attention owing to enormous threats to the Internet. Due to the rapid spreading of malicious worms, it is necessary to explore the integrated measures to automatically mitigate the propagation on the Internet. In this paper, a novel worm propagation model is established, which combines both impulsive quarantine and benign worm implementation. Then, sufficient conditions for the global stability of worm-free periodic solution and the permanence of the benign worm are obtained. Finally, the effects of quarantine strategy are assessed and some feasible strategies that can constrain the propagation of malicious worm are provided by numerical simulation.

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