Geodesic
The Impact of Hybrid Quarantine Strategies and Delay factor on Viral Prevalence in Computer Networks
Chang Li1 ; Xiaofeng Liao1
1 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 4, pp. 105-119 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

Recently, the quarantine approach, which has been applied to infectious disease control, is widely regarded as an effective measure to suppress viral spread in computer networks. Hence, in order to prevent the spread of computer virus in network, and consider the latent period of a latent computer, a new delayed epidemic model of computer virus with hybrid quarantine strategies is presented. By regarding the delay as bifurcating parameter and analyzing the associated characteristic equation, the dynamical behaviors, including local asymptotical stability in which the virus spreading can be controlled, and furthermore, local Hopf bifurcation occurs in the system, which implies computer virus is out of control, are investigated. By applying the normal form and center manifold theorem, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also determined. Some numerical simulations are provided to support our theoretical results which also imply that hybrid quarantine strategies can inhibit viral spread effectively, and make the model be asymptotically stable.
DOI : 10.1051/mmnp/201611408

Chang Li 1 ; Xiaofeng Liao 1

1 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China 
@article{10_1051_mmnp_201611408,
     author = {Chang Li and Xiaofeng Liao},
     title = {The {Impact} of {Hybrid} {Quarantine} {Strategies} and {Delay} factor on {Viral} {Prevalence} in {Computer} {Networks}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {105--119},
     year = {2016},
     volume = {11},
     number = {4},
     doi = {10.1051/mmnp/201611408},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611408/}
}
TY  - JOUR
AU  - Chang Li
AU  - Xiaofeng Liao
TI  - The Impact of Hybrid Quarantine Strategies and Delay factor on Viral Prevalence in Computer Networks
JO  - Mathematical modelling of natural phenomena
PY  - 2016
SP  - 105
EP  - 119
VL  - 11
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611408/
DO  - 10.1051/mmnp/201611408
LA  - en
ID  - 10_1051_mmnp_201611408
ER  - 
%0 Journal Article
%A Chang Li
%A Xiaofeng Liao
%T The Impact of Hybrid Quarantine Strategies and Delay factor on Viral Prevalence in Computer Networks
%J Mathematical modelling of natural phenomena
%D 2016
%P 105-119
%V 11
%N 4
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611408/
%R 10.1051/mmnp/201611408
%G en
%F 10_1051_mmnp_201611408
Chang Li; Xiaofeng Liao. The Impact of Hybrid Quarantine Strategies and Delay factor on Viral Prevalence in Computer Networks. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 4, pp. 105-119. doi: 10.1051/mmnp/201611408

[1] Y. Zhou, H. Liu Stability of periodic solutions for an SIS model with pulse vaccination Math. Comput. Model. 2003 299 308

[2] A. Economoua, A. Gómez-Corral, M. López-García A stochastic SIS epidemic model with heterogeneous contacts Phys. A 2015 78 97

[3] S. Gao, L. Chen, L. Sun Dynamic complexities in a seasonal prevention epidemic model with birth pulses Chaos Solitons & Fractals 2005 1171 1181

[4] X Han, Q. Tan Dynamical behavior of computer virus on internet Appl. Math. Comput. 2010 2520 2526

[5] B.K. Mishra, D.K. Saini SEIRS epidemic model with delay for transmission of malicious objects in computer network Appl. Math. Comput. 2007 1476 1482

[6] B.K. Mishra, N Jha SEIQRS model for the transmission of malicious objects in computer network Appl. Math. Model. 2010 710 715

[7] L. Yang, X. Yang The effect of infected external computers on the spread of viruses: a compartment modeling study Phys. A 2013 6523 6535

[8] L. Yang, X. Yang A new epidemic model of computer viruses Commun. Nonlinear Sci. 2014 1935 1944

[9] J. Ren, Y. Xu, J. Liu Investigation of dynamics of a virus-antivirus model in complex network Phys. A 2015 533 540

[10] T. Chen, N. Jamil Effectiveness of Quarantine in Worm Epidemics ICC 2006 2006 2142 2147

[11] V Yegneswaran, P Barford, D Plonka On the design and use of internet sinks for network abuse monitoring Lect. Notes Comput. Sc. 2004 146 165

[12] O Depren, M Topallar, E Anarim, M.K. Ciliz An intelligent intrusion detection system (IDS) for anomaly and misuse detection in computer networks Expert Syst. Appl. 2005 713 722

[13] P Sandhya, G Crina, T Johnson Modeling intrusion detection system using hybrid intelligent systems J. Netw. Comput. Appl. 2007 114 132

[14] M.A. Aydin, A.H. Zaim, K.G. Ceylan A hybrid intrusion detection system design for computer network security Comput. Electr. Eng. 2009 517 526

[15] C. Zou, G. Gong, D Towsley, Worm propagation modeling and analysis under dynamic quarantine defense. WORM 2003, Washington, DC, USA, (2003) 51–60.

[16] O. Toutonji, S.M. Yoo Passive Benign Worm Propagation Modeling with Dynamic Quarantine Defense. KSII T Internet Inf. Syst. 2009 96 107

[17] F. Wang, Y. Zhang, C. Wang, J. Ma, S.J. Moon Stability analysis of a SEIQV epidemic model for rapid spreading worms Comput. Secur. 2010 410 418

[18] Y Yao, L Guo, H Guo, G Yu, X. Gao, X. Tong Pulse quarantine strategy of internet worm propagation: Modeling and analysis Comput. Electr. Eng. 2012 1047 1061

[19] Y Yao, X. Feng, W Yang, W. Xiang, F. Gao Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy Math. Probl. Eng.

[20] Y.B. Kafai Understanding virtual epidemics: children's folk conceptions of a computer virus J. Sci. Educ. Technol. 2008 523 529

[21] H. Song, Q. Wang, W. Jiang Stability and Hopf Bifurcation of a Computer Virus Model with Infection Delay and Recovery Delay J. Appl. Math.

[22] J. Ren, Y. Xu Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability Math. Probl. Eng.

[23] T Dong, X. Liao, H. Li Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus Abstr. Appl. Anal.

[24] W. Wang, S.K. Nguang, S. Zhong, F Liu Novel delay-dependent stability criterion for time-varying delay systems with parameter uncertainties and nonlinear perturbations Inform. Sciences 2014 321 333

[25] Z. Zhang, H. Yang Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model The Scientific World J.

[26] T. Kmet, M. Kmetova Adaptive critic design and Hopfield neural network based simulation of time delayed photosynthetic production and prey-predator model Inform. Sciences 2015 586 599

[27] G. Wang, Q. Zhang, C. Yang Stabilization of singular Markovian jump systems with time-varying switchings Inform. Sciences 2015 254 270

[28] M. Yang, Z. Zhang, Q. Li, G. Zhang An SLBRS Model with Vertical Transmission of Computer Virus over the Internet Discrete Dyn. Nat. Soc.

[29] C. Gan, X. Yang Theoretical and experimental analysis of the impacts of removable storage media and antivirus software on viral spread Commun. Nonlinear Sci. 2015 167 174

[30] X. Li, J. Wei On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays Chaos Solitons & Fractals 2005 519 526

[31] B.D. Hassard, N.D. Kazarinoff, Y.H. Wan, Theory and Applications of Hopf Bifurcation. Cambridge Univ. Press. Cambridge, UK, 1981.

[32] J. Amador The stochastic SIRA model for computer viruses Appl. Math. Comput. 2014 1112 1124

[33] S. Xua, W. Lubc, H. Lic A Stochastic Model of Active Cyber Defense Dynamics Internet Math. 2015 23 61

[34] C. Deng, Q. Liu, A computer virus spreading model with nonlinear infectivity on scale-free network. ICISMME 2015, (2015) 1684–1688.

Cité par Sources :