Modeling and analysis of the spread of computer virus

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 12, 2012, Pages 5117-5124

  Zhu, Qingyi ^a   Yang, Xiaofan ^a   Ren, Jianguo ^a  

^a CHONGQING UNIVERSITY   (China)

Author keywords

Computer virus; Equilibrium; Global stability; Local stability; Propagation model

Indexed keywords

COMPUTATIONAL METHODS;

ANALYTICAL RESULTS; DYNAMICAL MODELING; EQUILIBRIUM; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; INFECTION FREE EQUILIBRIUM; LOCAL STABILITY; MODELLING AND ANALYSIS; PROPAGATION MODELS; QUALITATIVE ANALYSIS;

COMPUTER VIRUSES;

EID: 84864413758     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.05.030     Document Type: Article

References (19)

1. Barbashin E.A. Introduction to the theory of stability 1970, Walters-Noordhoff, Groningen.
2. Billings L., Spears W.M., Schwartz I.B. A unified prediction of computer virus spread in connected networks. Phys Lett A 2002, 297:261-266.
3. Cohen F. Computer viruses: theory and experiments. Comput Secur 1987, 6:22-35.
4. Freedman H.I., Ruan S., Tang M. Uniform persistence and flows near a closed positively invariant set. J Differ Eq 1994, 6:586-600.
5. Han X., Tan Q. Dynamical behavior of computer virus on Internet. Appl Math Comput 2010, 217:2520-2526.
6. Kephart JO, White SR. Directed-graph epidemiological models of computer viruses. In: Proceedings of the IEEE symposium on security and privacy; 1991. p. 343-59.
7. Kephart JO, White SR. Measuring and modeling computer virus prevalence. In: Proceedings of the IEEE symposium on security and privacy; 1993. p. 2-15.
8. Li M.Y., Muldowney J.S. Global stability of the SEIR model in expidemiology. Math Biosci 1995, 125:155-164.
9. Li M.Y., Muldowney J.S. A geometric approach to global stability problems. SIAM J Math Anal 1996, 27:155-164.
10. Martin R.H. Logarithmic norms and projections applied to linear differential systems. J Math Anal Appl 1974, 45:432-454.
11. Mishra B.K., Jha N. Fixed period of temporary immunity after run of anti-malicious software on computer nodes. Appl Math Comput 2007, 190:1207-1212.
12. Mishra B.K., Pandey S.K. Dynamic model of worms with vertical transmission in computer network. Appl Math Comput 2011, 217:8438-8446.
13. Piqueira J.R.C., Araujo V.O. A modified epidemiological model for computer viruses. Appl Math Comput 2009, 213:355-360.
14. Piqueira J.R.C., de Vasconcelos A.A., Gabriel C.E.C.J., Araujo V.O. Dynamic models for computer viruses. Comput Secur 2008, 27:355-359.
15. Ren J., Yang X., Yang L., Xu Y., Yang F. A delayed computer virus propagation model and its dynamics. Chaos Soliton Fract 2012, 45:74-79.
16. Ren J., Yang X., Zhu Q., Yang L., Zhang C. A novel computer virus model and its dynamics. Nonlinear Anal-Real 2012, 3:376-384.
17. Thieme H.R. Asymptotically autonomous differential equations in the plane. Rocky Mt J Math 1994, 24:351-380.
18. Wierman J.C., Marchette D.J. Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction. Comput Stat Data An 2004, 45:3-23.
19. Yuan H., Chen G. Network virus-epidemic model with the point-to-group information propagation. Appl Math Comput 2008, 206:357-367.