zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stability analysis of VEISV propagation modeling for network worm attack. (English) Zbl 1246.68067
Summary: We propose the VEISV (vulnerable-exposed-infectious-secured-vulnerable) network worm attack model, which is appropriate for measuring the effects of security countermeasures on worm propagation. Contrary to existing models, our model takes into consideration accurate positions for dysfunctional hosts and their replacements in state transition. Using the reproduction rate, we derive global stability of a worm-free state and local stability of a unique worm-epidemic state. Furthermore, simulation results show the positive impact of increasing security countermeasures in the vulnerable state on worm-exposed and infectious propagation waves. Finally, equilibrium points are confirmed by phase plots.

68M11Internet topics
68M10Network design and communication of computer systems
34C60Qualitative investigation and simulation of models (ODE)
34D23Global stability of ODE
Full Text: DOI
[1] Moore, D.; Paxson, V.; Savage, S.; Shannon, C.; Staniford, S.; Weaver, N.: Inside the slammer worm, IEEE magaz. Secur. privacy 1, No. 4, 33-39 (2003)
[2] D. Moore, C. Shannon, J. Brown, Code red: a Case Study on the Spread and Victims of an Internet Worm, in: Proceedings of the 2nd ACM SIGCOMM Workshop on Internet Measurement, Marseille, France, Nov. 2002, pp. 273 -- 284.
[3] (eEye Digital Security Research) R. Permeh, M. Maiffret, Analysis:.ida”Code Red” Worm. <http://research.eeye.com/html/advisories/published/AL20010717.html>, 2001 (accessed 17.07.01).
[4] (The Cooperative Association for Internet Data Analysis) D. Moore, C. Shannon, The Spread of the Code-Red Worm (CRv2). <http://www.caida.org/research/security/code-red/coderedv2_analysis.xml>, 2008 (accessed 18.11.08).
[5] M.R. Faghani, H. Saidi, Social networks’ XSS worms, in: Proceedings of the International Conference Computational Science and Engineering, CSE ’09, vol. 4, 29 -- 31 Aug. 2009, pp. 1137 -- 1141.
[6] (SRI International) P. Porras, et al., An Analysis of Conficker’s Logic and Rendezvous Points [Technical Report]. <http://mtc.sri.com/Conficker/>, 2009 (accessed 19.03.09).
[7] (BT Managed Security Solutions Group) Risk Assessment: W32.Conficker.C. <http://bt.counterpane.com/BT_MSSG_RA_Conficker.C_Update2.pdf>, 2009 (accessed 30.03.09).
[8] (CIO Digest Online Extras)A. Drummer. Thoreau,Conficker: The Battle for Everyman, July, 2009.<http://eval.symantec.com/mktginfo/enterprise/articles/b-ciodigest_june09_conficker.en-us.pdf>.
[9] Yu, W.; Zhang, N.; Fu, X.; Zhao, W.: Self-disciplinary worms and countermeasures: modeling and analysis, IEEE trans. Parallel distrib. Syst. 21, No. 10, 1501-1514 (2010)
[10] Y. Yao, J.W. Lv, F.X. Gao, G. Yu, Q.X. Deng, Modeling the cooperation between malicious codes, in: Proceedings of the International Conference E-Business and Information System Security, EBISS ’0, 23 -- 24 May. 2009, pp. 1 -- 5.
[11] R. Li, L. Gan, Y. Jia, Propagation model for botnet based on conficker monitoring, in: Proceedings of the Second International Symposium, Information Science and Engineering, ISISE’09, 26 -- 28 Dec. 2009, pp. 185 -- 190.
[12] Friedman, A.: Good neighbors can make good fences: a peer-to-peer user security system, IEEE technol. Soc. magaz. 26, No. 1, 17-24 (2007)
[13] Yuan, H.; Chen, G.: Network virus-epidemic model with the point-to-group information propagation, Appl. math. Comput. 206, 357-367 (2008) · Zbl 1162.68404 · doi:10.1016/j.amc.2008.09.025
[14] Merkin, D. R.: An introduction to theory of stability, (1997) · Zbl 0890.92029
[15] Robinson, R. C.: An introduction to dynamical system: continuous and discrete, (2004) · Zbl 1073.37001
[16] Kim, J.; Radhakrishana, S.; Jang, J.: Cost optimization in SIS model of worm infection, Etri j. 28, No. 5, 692-695 (2006)
[17] H. Zhou, Y. Wen, H. Zhao, Modeling and analysis of active benign worms and hybrid benign worms containing the spread of worms, in: Proceedings of the IEEE International Conference on Networking (ICN’07), 2007.
[18] Kim, J.; Radhakrishnan, S.; Jang, J.: Cost optimization in SIS model of worm infection, Etri j. 28, No. 5, 692-695 (2006)
[19] M.H.R. Khouzani, S. Sarkar, E. Altman, Maximum damage malware attack in mobile wireless networks, in: IEEE Proceedings, INFOCOM’10, 14 -- 19 Mar. 2010, pp. 1 -- 9.
[20] Li, X. Z.; Zhou, L. L.: Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate, Chaos soliton. Fract. 40, 874-884 (2007) · Zbl 1197.34077 · doi:10.1016/j.chaos.2007.08.035
[21] Li, G.; Zhen, J.: Global stability of an SEI epidemic model with general contact rate, Chaos soliton. Fract. 23, 997-1004 (2004) · Zbl 1062.92062 · doi:10.1016/j.chaos.2004.06.012
[22] Mishra, B. K.; Jha, N.: Fixed period of temporary immunity after run of anti-malicious software on computer nodes, Appl. math. Comput. 190, 1207-1212 (2007) · Zbl 1117.92052 · doi:10.1016/j.amc.2007.02.004
[23] Mishra, B. K.; Jha, N.: SEIQRS model for the transmission of malicious objects in computer network, Appl. math. Modell. 34, 1207-1212 (2009) · Zbl 1117.92052
[24] Yi, N.; Zhang, Q.; Mao, K.; Yang, D.; Li, Q.: Analysis and control of an SEIR epidemic system with nonlinear transmission rate, Math. comput. Modell. 50, 1498-1513 (2009) · Zbl 1185.93101 · doi:10.1016/j.mcm.2009.07.014
[25] Sun, C.; Lin, Y.; Tang, S.: Global stability for an special SEIR epidemic model with nonlinear incidence rates, Chaos soliton. Fract. 33, 290-297 (2007) · Zbl 1152.34357 · doi:10.1016/j.chaos.2005.12.028
[26] Jin, Y.; Wang, W.; Xiao, S.: An SIRS model with a nonlinear incidence rate, Chaos soliton. Fract. 34, 1482-1497 (2007) · Zbl 1152.34339 · doi:10.1016/j.chaos.2006.04.022
[27] Q. Liu, R. Xu, S. Wang, Modelling and analysis of an SIRS model for worm propagation, in: Proceedings of the International Conference Computational Intelligence and Security, CIS ’09, vol. 2, 11 -- 14 Dec. 2009, pp. 361 -- 365.
[28] Wang, F.; Zhang, Y.; Wang, C.; Ma, J.; Moon, S.: Stability analysis of SEIQV epidemic model for rapid spreading worms, Comput. secur. 29, 410-418 (2010)
[29] C.C. Zou, W. Gong, D. Towsley, Code red worm propagation modeling and analysis, in: 9th ACM Symposium on Computer and Communication Security, Washington DC, 2002, pp. 138 -- 147.
[30] Z. Chen, L. Gao, K. Kwiat, Modeling the spread of active worms, in: Proceedings of the IEEE INFOCOM, vol. 3, 2003, pp. 1890 -- 1900.
[31] W. Yang, W. Ying, G.R. Chang, Z.Q. Zhang, Research on the epidemic model in P2P file-sharing system, in: Proceedings of the Ninth International Conference on Hybrid Intelligent Systems, HIS ’09, vol. 2, 12 -- 14 Aug. 2009, pp. 386 -- 390.
[32] D. Moore, C. Shannon, G.M. Voelker, S. Savage, Internet quarantine: requirements for containing self-propagating code, in: Proceedings of the IEEE INFOCOM, San Franciso, vol. 3, March -- April 2003, pp. 1901 -- 1910.
[33] F. Burckhardt, Modeling infections deceases in virtual realties, in: Proceedngs of the 24th Chaos Communication Congress, 2007.
[34] C.C. Zou, W. Gong, D. Towsley, Worm propagation modeling and analysis under dynamic quarantine defense, in: Proceedings of the 2003 ACM Workshop on Rapid Malcode (WORM’03), Washington, DC, Oct. 2003.
[35] Hurwitz, A.: On the conditions under which an equation has only roots with negative real parts, Rpt. in selected papers on mathematical trends in control theory (1964)
[36] C. Shannon, D. Moore, The Spread of the Code-Red Worm. <http://www.caida.org/analysis/security/code-red/coderedv2_analysis.xml>.
[37] (Panda Securlity) Six percent of computers scanned by Panda Security are infected by the conficker worm [20th Anniversary 1990-2010 Report]. <http://www.pandasecurity.com/homeusers/media/press-releases/viewnews?noticia=9526>, 2009 (accessed 21.01.09).