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Song, Li-Peng; Han, Xie; Liu, Dong-Ming; Jin, Zhen

Adaptive human behavior in a two-worm interaction model. (English) Zbl 1253.68051

Discrete Dyn. Nat. Soc. 2012, Article ID 828246, 13 p. (2012).
Summary: The complex interactions among internet worms have great impact on the dynamics of worms. To contain the propagation of worms, it is necessary to characterize these interactions. Therefore, a two-worm interaction model is presented in this paper. Different from previous researches, we have considered the influence of adaptive human reaction stirred by one cooperative worm on the other worm in the model. The model’s equilibria and their stability conditions are obtained mathematically and verified by simulations. Results indicate that considering adaptive human behavior significantly changes the prospective propagation course of worms and that this consideration has implications for designing counterworm methods.

Cited in 3 Documents

MSC:

68M11 Internet topics
68M10 Network design and communication in computer systems
91D30 Social networks; opinion dynamics

Keywords:

internet worms; dynamics; propagation; two-worm interaction model; adaptive human reaction
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References:

[1] Kaspersky Security Bulletin. Monthly Malware Statistics, February 2012, http://www.securelist.com/en/analysis/204792223 .
[2] J. R. Crandall, R. Ensafi, S. Forrest, J. Ladau, and B. Shebaro, “The ecology of malware,” in Proceedings of the New Security Paradigms Workshop (NSPW ’08), pp. 99-106, September 2008. · doi:10.1145/1595676.1595692
[3] X. Han and Q. Tan, “Dynamical behavior of computer virus on Internet,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2520-2526, 2010. · Zbl 1209.68139 · doi:10.1016/j.amc.2010.07.064
[4] L.-P. Song, Z. Jin, G.-Q. Sun, J. Zhang, and X. Han, “Influence of removable devices on computer worms: dynamic analysis and control strategies,” Computers & Mathematics with Applications, vol. 61, no. 7, pp. 1823-1829, 2011. · Zbl 1219.37065 · doi:10.1016/j.camwa.2011.02.010
[5] B. K. Mishra and S. K. Pandey, “Dynamic model of worms with vertical transmission in computer network,” Applied Mathematics and Computation, vol. 217, no. 21, pp. 8438-8446, 2011. · Zbl 1219.68080 · doi:10.1016/j.amc.2011.03.041
[6] J. Ren, X. Yang, Q. Zhu, L.-X. Yang, and C. Zhang, “A novel computer virus model and its dynamics,” Nonlinear Analysis, vol. 13, no. 1, pp. 376-384, 2012. · Zbl 1238.34076 · doi:10.1016/j.nonrwa.2011.07.048
[7] L. Feng, X. Liao, H. Li , et al., “Hopf bifurcation analysis of a delayed viral infection model in computer networks,” Mathematical and Computer Modeling, vol. 56, no. 7, pp. 167-179, 2012. · Zbl 1255.34071
[8] L.-X. Yang and X. Yang, “Propagation behavior of virus codes in the situation that infected computers are connected to the internet with positive probability,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 693695, 13 pages, 2012. · Zbl 1248.68077 · doi:10.1155/2012/693695
[9] Q. Zhu, X. Yang, and J. Ren, “Modeling and analysis of the spread of computer virus,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 5117-5124, 2012. · Zbl 1261.93012
[10] Y. Li, J.-X. Pan, and Z. Jin, “Dynamic modeling and analysis of the email virus propagation,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 472072, 22 pages, 2012. · Zbl 1248.90033 · doi:10.1155/2012/472072
[11] S. Tanachaiwiwat and A. Helmy, “Encounter-based worms: analysis and defense,” Ad Hoc Networks, vol. 7, no. 7, pp. 1414-1430, 2009. · doi:10.1016/j.adhoc.2009.02.004
[12] L. P. Song, Z. Jin, and G. Q. Sun, “Modeling and analyzing of botnet interactions,” Physica A, vol. 390, no. 2, pp. 347-358, 2010. · doi:10.1016/j.physa.2010.10.001
[13] Kaspersky Lab: Securelist, http://www.securelist.com/en/descriptions/old21944.
[14] J. D. Murray, Mathematical Biology, Springer, Berlin, Germany, 2003. · Zbl 1006.92002
[15] W. H. Debany, “Modeling the spread of internet worms via persistently unpatched hosts,” IEEE Network, vol. 22, no. 2, pp. 26-32, 2008.
[16] E. A. Barbashin, Introduction to the Theory of Stability, Wolters-Noordhoff Publishing, Groningen, The Netherlands, 1970. · Zbl 0198.19703
[17] S. Funk, M. Salathé, and V. A. A. Jansen, “Modelling the influence of human behaviour on the spread of infectious diseases: a review,” Journal of the Royal Society Interface, vol. 7, no. 50, pp. 1247-1256, 2010. · doi:10.1098/rsif.2010.0142
[18] E. P. Fenichel, C. Castillo-Chavez, and M.G. Ceddia, “Adaptive human behavior in epidemiological models,” Proceedings of the National Academy of Sciences of United States of America, vol. 108, no. 15, pp. 6306-6311, 2011.
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