Dynamical analysis and control strategies on malware propagation model

Applied Mathematical Modelling

Volumn 37, Issue 16-17, 2013, Pages 8225-8236

  Feng, Liping ^a,b   Liao, Xiaofeng ^a   Han, Qi ^c   Li, Huaqing ^a  

^a CHONGQING UNIVERSITY   (China)

^b Department of Computer Science and Technology of Xinzhou Normal University ^*  (China)

^c CHONGQING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Malware

Indexed keywords

BASIC REPRODUCTIVE NUMBER; BIFURCATION PARAMETER; DYNAMICAL ANALYSIS; DYNAMICAL BEHAVIORS; MALICIOUS SOFTWARE; MALWARE PROPAGATION; MALWARES; SUFFICIENT CONDITIONS;

COMPUTER SIMULATION; DELAY CONTROL SYSTEMS; HOPF BIFURCATION; TIME DELAY;

COMPUTER CRIME;

EID: 84881544095     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.03.051     Document Type: Article

References (31)

1. M. Garetto, W.B. Gong, D. Towsley, Modeling malware spreading dynamics, in: Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications (INFOCOM 2003), vol. 3, 2003, pp. 1869-1879.
2. S. Datta, H. Wang, The effectiveness of vaccinations on the spread of email-borne computer viruses, in: Proceedings of the Conference on Electrical and, Computer Engineering, 2005, pp. 219-223.
3. Bernoulli D. Essai d'une nouvelle analyse de la mortalité causée la petite vérole et des avantages de l'inoculation pour la prévenir. Mém. Math. Phys. Acad. Roy. Sci. Paris 1760, 1-45.
4. Bailey N.T.J. The Mathematical Theory Of Infectious Diseases and its Applications 1975, Oxford University Press, New York.
5. J.O. Kephart, S.R. White, Directed-graph epidemiological models of computer viruses, in: Proceedings of the IEEE Computer Society Symposium on Security and Privacy, 1991, pp. 343-359.
6. J.O. Kephart, S.R. White, Measuring and modeling computer virus prevalence, in: Proceedings of the IEEE Computer Society Symposium on Security and Privacy, 1993, pp. 2-15.
7. Billings L., Spears W.M., Schwartz I.B. A unified prediction of computer virus spread in connected networks. Phys. Lett. A 2002, 297(3):261-266.
8. Zou C.C., Gong W.B., Towsley D., Gao L.X. The monitoring and early detection of internet worms. IEEE-ACM Trans. Networking 2005, 13(5):961-974.
9. Zou C.C., Towsley D., Gong W.B. On the performance of Internet worm scanning strategies. Perform. Eval. 2006, 63(7):700-723.
10. C.C. Zou, D. Towsley, W.B. Gong, S.l. Cai, Routing worm: A fast, selective attack worm based on IP address information, in: Proceedings of the 19th Workshop on Principles of Advanced and Distributed, Simulation, 2005, pp. 199-206.
11. Zou C.C., Towsley D., Gong W.B. Modeling and simulation study of the propagation and defense of Internet email worm. IEEE Trans. Dependable Secure Comput. 2007, 4(2):105-118.
12. Daley D.J., Gani J. Epidemic Modeling: An Introduction 1999, Cambridge University Press, New York.
13. Kermack W.O., McKendrick A.G. Contributions to the mathematical theory of epidemics. Bull. Math. Biol. 1991, 53(1):33-55.
14. Bimal K.M., Dinesh K.S. SEIRS epidemic model with delay for transmission of malicious objects in computer network. Appl. Math. Comput. 2007, 188(2):1476-1482.
15. Xu R., Ma Z.E., Wang Z.P. Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity. Comput. Math. Appl. 2010, 59(9):3211-3221.
16. Han X., Tan Q.L. Dynamical behavior of computer virus on Internet. Appl. Math. Comput. 2010, 217(6):2520-2526.
17. Song L.P., Jin Z., Sun G.Q., Zhang J., Han X. Influence of removable devices on computer worms: dynamic analysis and control strategies. Comput. Math. Appl. 2011, 61(7):1823-1829.
18. Wang S.J., Liu Q.M., Yu X.F., Ma Y. Bifurcation analysis of a model for network worm propagation with time delay. Math. Comput. Model. 2010, 52(3):435-447.
19. Bimal K.M., Samir K.P. Fuzzy epidemic model for the transmission of worms in computer network. Nonlinear Anal.: Real World Appl. 2010, 11(5):4335-4341.
20. Chen Z.S., Ji C.Y. Spatial-temporal modeling of malware propagation in networks. IEEE Trans. Neural Networks 2005, 16(5):1291-1303.
21. Anagnostopoulos C., Hadjiefthymiades S., Zervas E. Information dissemination between mobile nodes for collaborative context awareness. IEEE Trans. Mobile Comput. 2011, 10(12):1710-1725.
22. C.C. Zou, W. Gong, D. Towsley, Code red worm propagation modeling and analysis, in: Proceedings of the 9th ACM Conference on Computer and Communications, Security, 2002, pp 138-147.
23. J. Cowie, A. Ogielski, Global routing instabilities during code red II and Nimda worm propagation, 2001. http://www.renesys.com/tech/presentations/.
24. L. Wang, X. Zhao, D. Pei, R. Bush, D. Massey, A. Mankin, S. Wu, L. Zhang, Observation and analysis of BGP behavior under stress, in: Proceedings of the 2nd ACM SIGCOMM Workshop on Internet, measurement, 2002, pp. 183-195.
25. J. Cowie, A. Hobgood, R. Meharwal, The curious incident of 7 NOV 2011. http://www.renesys.com/tech/presentations/.
26. Feng L.P., Liao X.F., Li H.Q., Han Q. Hopf bifurcation analysis of a delayed viral infection model in computer networks. Math. Comput. Model. 2012, 56:167-179.
27. Moghadas S.M., Gumel A.B. Global stability of a two-stage epidemic model with generalized non-linear incidence. Math. Comput. Simul. 2002, 60(1):107-118.
28. Saini D.K. A mathematical model for the effect of malicious object on computer network immune system. Appl. Math. Model. 2011, 35(8):3777-3787.
29. Hale J., Lunel S.M. Introduction to Functional Differential Equations 1993, Springer-Verlag.
30. Li H.Q., Liao F.X., Liao R.J. A unified approach to chaos suppressing and inducing in a periodically forced family of nonlinear oscillators. IEEE Trans. Circuits Syst. - I: Regular Papers 2012, 59(4):784-795.
31. Li H.Q., Liao F.X., Saleem U., Xiao L. Analytical proof on the existence of chaos in the generalized Duffing-type oscillator with fractional-order deflection. Nonlinear Anal. Ser. B: Real World Appl. 2012, 13(6):2724-2733.