Analysis of a delayed internet worm propagation model with impulsive quarantine strategy

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Yao, Yu ^a,b   Feng, Xiaodong ^a,b   Yang, Wei ^c   Xiang, Wenlong ^a,b   Gao, Fuxiang ^a,b  

^a NORTHEASTERN UNIVERSITY   (China)

^b NORTHEASTERN UNIVERSITY   (China)

^c Northeastern University   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER WORMS; HOPF BIFURCATION; TIME DELAY;

INHIBITION EFFECT; INTERNET WORM; NUMERICAL EXPERIMENTS; WORM PROPAGATION; WORM PROPAGATION MODELS;

INTERNET;

EID: 84901045200     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/369360     Document Type: Article

References (27)

1. Qing S., Wen W., A survey and trends on internet worms. Computers and Security 2005 24 4 334 346 2-s2.0-19944374456 10.1016/j.cose.2004.10.001 (Pubitemid 40752316)
2. Anderson R. M., May R. M., Infected Diseases of Human, Dynamics and Control 1992 Oxford, UK Oxford University Press
3. Zhu Q., Yang X., Ren J., Modeling and analysis of the spread of computer virus. Communications in Nonlinear Science and Numerical Simulation 2012 17 12 5117 5124 10.1016/j.cnsns.2012.05.030 MR2960303 ZBL1261.93012
4. Mishra B. K., Pandey S. K., Fuzzy epidemic model for the transmission of worms in computer network. Nonlinear Analysis: Real World Applications 2010 11 5 4335 4341 2-s2.0-77955517848 10.1016/j.nonrwa.2010.05.018
5. Mishra B. K., Pandey S. K., Dynamic model of worms with vertical transmission in computer network. Applied Mathematics and Computation 2011 217 21 8438 8446 10.1016/j.amc.2011.03.041 MR2802253 ZBL1219.68080
6. Ren J., Yang X., Zhu Q., Yang L.-X., Zhang C., A novel computer virus model and its dynamics. Nonlinear Analysis: Real World Applications 2012 13 1 376 384 10.1016/j.nonrwa.2011.07.048 MR2846848 ZBL1238.34076
7. Yin S., Ding S. X., Haghani A., Hao H., Zhang P., A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process. Journal of Process Control 2012 22 9 1567 1581 10.1016/j.jprocont.2012.06.009
8. Yin S., Ding S. X., Sari A. H. A., Hao H., Data-driven monitoring for stochastic systems and its application on batch process. International Journal of Systems Science 2013 44 7 1366 1376 10.1080/00207721.2012.659708 MR3050076 ZBL1278.93259
9. Yin S., Hao L., Ding S., Real-time implementation of fault-tolerant control systems with performance optimization. IEEE Transactions on Industrial Electronics 2013 61 5 2402 2411
10. Yang L.-X., Yang X., Zhu Q., Wen L., A computer virus model with graded cure rates. Nonlinear Analysis: Real World Applications 2013 14 1 414 422 10.1016/j.nonrwa.2012.07.005 MR2969844 ZBL1258.68020
11. Zou C. C., Gong W., Towsley D., Code red worm propagation modeling and analysis. Proceedings of the 9th ACM Conference on Computer and Communications Security November 2002 ACM 138 147 2-s2.0-0038349210
12. Zou C. C., Gong W., Towsley D., Worm propagation modeling and analysis under dynamic quarantine defense. Proceedings of the ACM Workshop on Rapid Malcode (WORM '03) October 2003 ACM 51 60 2-s2.0-14944368398 (Pubitemid 40681810)
13. Yao Y., Xie X.-W., Guo H., Yu G., Gao F.-X., Tong X.-J., Hopf bifurcation in an Internet worm propagation model with time delay in quarantine. Mathematical and Computer Modelling 2013 57 11-12 2635 2646 2-s2.0-79960561776 10.1016/j.mcm.2011.06.044
14. Yao Y., Xiang W., Qu A., Yu G., Gao F., Hopf bifurcation in an SEIDQV worm propagation model with quarantine strategy. Discrete Dynamics in Nature and Society 2012 2012 18 10.1155/2012/304868 304868 MR3000407 ZBL1253.68052
15. Yao Y., Guo L., Guo H., Yu G., Gao F.-X., Tong X.-J., Pulse quarantine strategy of internet worm propagation: modeling and analysis. Computers and Electrical Engineering 2012 38 5 1047 1061 2-s2.0-80052216680 10.1016/j.compeleceng.2011.07.009
16. Wang F., Zhang Y., Wang C., Ma J., Moon S., Stability analysis of a SEIQV epidemic model for rapid spreading worms. Computers and Security 2010 29 4 410 418 2-s2.0-77951206095 10.1016/j.cose.2009.10.002
17. Huo H.-F., Ma Z.-P., Dynamics of a delayed epidemic model with non-monotonic incidence rate. Communications in Nonlinear Science and Numerical Simulation 2010 15 2 459 468 10.1016/j.cnsns.2009.04.018 MR2572576 ZBL1221.34197
18. Zhang C., Liu W., Xiao J., Zhao Y., Hopf bifurcation of an improved SLBS model under the influence of latent period. Mathematical Problems in Engineering 2013 2013 10 196214 10.1155/2013/196214
19. Zhang Z., Yang H., Stability and Hopf bifurcation in a delayed SEIRS worm model in computer network. Mathematical Problems in Engineering 2013 2013 9 10.1155/2013/319174 319174 MR3132202
20. Ren J., Yang X., Yang L.-X., Xu Y., Yang F., A delayed computer virus propagation model and its dynamics. Chaos, Solitons & Fractals 2012 45 1 74 79 10.1016/j.chaos.2011.10.003 MR2863589 ZBL06196114
21. Li C.-H., Tsai C.-C., Yang S.-Y., Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay. Communications in Nonlinear Science and Numerical Simulation 2012 17 9 3696 3707 10.1016/j.cnsns.2012.01.018 MR2914003 ZBL1251.92036
22. Hassard B. D., Kazarinoff N. D., Wan Y. H., Theory and Applications of Hopf Bifurcation 1981 41 Cambridge, Mass, USA Cambridge University Press v+311 pp. (microfiche insert) London Mathematical Society Lecture Note Series MR603442
23. Dong T., Liao X., Li H., Stability and Hopf bifurcation in a computer virus model with multistate antivirus. Abstract and Applied Analysis 2012 2012 16 10.1155/2012/841987 841987
24. Bainov D. D., Simeonov P. S., Impulsive Differential Equations: Periodic Solutions and Applications 1993 Harlow, UK Longman
25. Lakshmikantham V., Banov D. D., Simeonov P. S., Theory of Impulsive Differential Equations 1989 6 Teaneck, NJ, USA World Scientific Publishing xii+273 Series in Modern Applied Mathematics MR1082551
26. Kuang Y., Delay Differential Equations with Applications in Population Dynamics 1993 191 Boston, Mass, USA Academic Press xii+398 Mathematics in Science and Engineering MR1218880
27. Gao S., Teng Z., Xie D., The effects of pulse vaccination on SEIR model with two time delays. Applied Mathematics and Computation 2008 201 1-2 282 292 10.1016/j.amc.2007.12.019 MR2432603 ZBL1143.92024