×

Influence of removable devices on computer worms: dynamic analysis and control strategies. (English) Zbl 1219.37065

Summary: Worms spreading via both Web-based scanning and removable devices account for a major part of threats on internet. However, their dynamical behavior and controlling methods remain unclear. As a result, we present a computer worm model incorporating specific features unique to those worms, in this paper. The threshold value \(R_{0}\) determining whether the worms die out is obtained. Theoretical analysis shows that if \(R_{0}<1\) the disease-free equilibrium is globally asymptotically stable; otherwise, the disease will be prevalent. Additionally, some control strategies are given. Our results are illustrated by numerical simulations.

MSC:

37N35 Dynamical systems in control
68M11 Internet topics
34D23 Global stability of solutions to ordinary differential equations
94A13 Detection theory in information and communication theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Security spotlight: understanding USB malware, 2010 [Online]. Available: http://us.trendmicro.com/imperia/md/content/us/trendwatch/researchandanalysis/56understandingusbmalwareapril192010.pdf; Security spotlight: understanding USB malware, 2010 [Online]. Available: http://us.trendmicro.com/imperia/md/content/us/trendwatch/researchandanalysis/56understandingusbmalwareapril192010.pdf
[2] Dan Raywood, Greater manchester police hit by conficker from infected USB that leaves it unconnected from its network for three days, SC Magazine February 2, 2010.; Dan Raywood, Greater manchester police hit by conficker from infected USB that leaves it unconnected from its network for three days, SC Magazine February 2, 2010.
[3] National computer virus emergency response center: report, 2009 (in Chinese) [Online]. Available:http://www.antivirus-china.org.cn/head/diaocha2009/report2009.doc; National computer virus emergency response center: report, 2009 (in Chinese) [Online]. Available:http://www.antivirus-china.org.cn/head/diaocha2009/report2009.doc
[4] Billings, L.; Spears, W. M.; Schwartz, I. B., A unified prediction of computer virus spread in connected networks, Physics Letters A, 297, 261-266 (2002) · Zbl 0995.68007
[5] Wierman, J. C.; Marchette, D. J., Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction, Computational Statistics and Data Analysis, 45, 3-23 (2004) · Zbl 1429.68037
[6] Mishra, B. K.; Saini, D., Mathematical models on computer viruses, Applied Mathematics and Computation, 187, 929-936 (2007) · Zbl 1120.68041
[7] Piqueira, J.; Vasconcelos, A.; Gabriel, C.; Araujo, V., Dynamic models for computer viruses, Computers and Security, 27, 355-359 (2008)
[8] Newman, M. E.J.; Forrest, S.; Balthrop, J., Email networks and the spread of computer viruses, Physical Review E, 66 (2002)
[9] Tanachaiwiwat, P.; Helmy, A., Encounter-based worms: analysis and defense, Ad Hoc Networks, 7, 1414-1430 (2009)
[10] Song, L. P.; Jin, Z.; Sun, G. Q., Modeling and analyzing of botnet interactions, Physica A, 390, 347-358 (2011)
[11] Lewis, M.; Renclawowicz, J.; Van den Driessche, P., Traveling waves and spread rates for a West Nile virus model, Bulletin of Mathematical Biology, 68, 3-23 (2006) · Zbl 1334.92414
[12] Markus, L., Asymptotically autonomous differential systems, (Lefschetz, S., Contributions to the Theory of Nolinear Oscillations III. Contributions to the Theory of Nolinear Oscillations III, Annals of Mathematics Studies, vol. 36 (1956)), 17-29 · Zbl 0075.27002
[13] Thieme, H. R., Asymptotically autonomous differential equations in the plane, Journal of Mathematics, 24, 351-380 (1994) · Zbl 0811.34036
[14] Anderson, R. M.; May, R. M., Infectious Diseases in Humans: Dynamics and Control (1991), Oxford University Press: Oxford University Press Oxford
[15] Barbashin, E. A., Introduction to the Theory of Stability (1970), Walters-Noordhoff: Walters-Noordhoff Groningen · Zbl 0198.19703
[16] Salle, J. La; Lefschetz, S., Stability by Liapunovs Direct Method (1961), Academic Press: Academic Press New York · Zbl 0098.06102
[17] Science and technology daily 2010 (in Chinese) [Online]. Available: http://www.stdaily.com/kjrb/content/2010-08/18/content220190.htm; Science and technology daily 2010 (in Chinese) [Online]. Available: http://www.stdaily.com/kjrb/content/2010-08/18/content220190.htm
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.