A propagation model of computer virus with nonlinear vaccination probability

Communications in Nonlinear Science and Numerical Simulation

Volumn 19, Issue 1, 2014, Pages 92-100

  Gan, Chenquan ^a,b   Yang, Xiaofan ^a   Liu, Wanping ^b   Zhu, Qingyi ^b  

^a SOUTHWEST UNIVERSITY   (China)

^b CHONGQING UNIVERSITY   (China)

Author keywords

Computer virus; Equilibrium; Global stability; Nonlinear vaccination probability; Propagation model

Indexed keywords

COMPUTER VIRUSES; NONLINEAR ANALYSIS; VACCINES;

BASIC REPRODUCTION NUMBER; COMPUTER VIRUS PROPAGATION; EQUILIBRIUM; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; NONLINEAR VACCINATION PROBABILITY; PARAMETER ANALYSIS; PROPAGATION MODELS; QUALITATIVE ANALYSIS; VACCINATION STRATEGY;

PROBABILITY;

EID: 84884139465     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2013.06.018     Document Type: Article

References (43)

1. Szor P. The art of computer virus research and defense 2005, Addison-Wesley Education Publishers Inc.
2. Kephart JO, White SR. Directed-graph epidemiological models of computer viruses. In: Proceedings of 1991 IEEE computer society symposium research in security and privacy; 1991, p. 343-59.
3. Tippett PS. The kinetics of computer viruses replication: a theory and preliminary survey. In: Safe Computing: Proceedings of fourth annual computer virus and security conference, New York; March 1991, p. 66-87.
4. Cohen F. Computer viruses: theory and experiments. Comput Secur 1987, 6(1):22-35.
5. Murray W.H. The application of epidemiology to computer viruses. Comput Secur 1988, 7(2):130-150.
6. Kephart J.O., White S.R., Chess D.M. Computers and epidemiology. IEEE Spectr 1993, 20-26.
7. 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.
8. Mishra B.K., Saini D.K. SEIRS epidemic model with delay for transmission of malicious objects in computer network. Appl Math Comput 2007, 188:1476-1482.
9. 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(7-8):355-359.
10. Piqueira J.R.C., Araujo V.O. A modied epidemiological for computer viruses. Appl Math Comput 2009, 213:355-360.
11. Han X., Tan Q.L. Dynamical behavior of computer virus on internet. Appl Math Comput 2010, 217:2520-2526.
12. Mishra B.K., Jha N. SEIQRS model for the transmission of malicious objects in computer network. Appl Math Model 2010, 34:710-715.
13. Mishra B.K., Pandey S.K. Fuzzy epidemic model for the transmission of worms in computer network. Nonlinear Anal Real 2010, 11:4335-4341.
14. Wang F.W., Zhang Y.K., Wang C.G., Ma J.F., Moon S.J. Stability analysis of a SEIQV epidemic model for rapid spreading worms. Comput Secur 2010, 29:410-418.
15. 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.
16. Mishra B.K., Pandey S.K. Dynamic model of worms with vertical transmission in computer network. Appl Math Comput 2011, 217:8438-8445.
17. Dong T., Liao X., Li H. Stability and Hopf bifurcation in a computer virus model with multistate antivirus. Abstr Appl Anal 2012, 2012. (Article ID 841987).
18. Feng L., Liao X., Li H., Han Q. Hopf bifurcation analysis of a delayed viral infection model in computer networks. Math Comput Model 2012, 56(7-8):167-179.
19. Ren J., Yang X., Yang L.X., Xu Y., Yang F. A delayed computer virus propagation model and its dynamics. Chaos Soliton Fractal 2012, 45:74-79.
20. Ren J., Yang X., Zhu Q., Yang L.X., Zhang C. A novel computer virus model and its dynamics. Nonlinear Anal Real 2012, 13:376-384.
21. Ren J., Xu Y., Zhang Y., Dong Y., Hao G. Dynamics of a delay-varying computer virus propagation model. Discrete Dyn Nat Soc 2012, 2012:1-12. (Article ID 371792).
22. Song L.-P., Han X., Liu D.-M., Jin Z. Adaptive human behavior in a two-worm interaction model. Discrete Dyn Nat Soc 2012, 2012:1-13. (Article ID 828246).
23. Yang L.-X., Yang X., Wen L., Liu J. A novel computer virus propagation model and its dynamics. Int J Comput Math 2012, 89(17):2307-2314.
24. Yang L.-X., Yang X. Propagation behavior of virus codes in the situation that infected computers are connected to the Internet with positive probability. Discrete Dyn Nat Soc 2012, 2012:1-13. (Article ID 693695).
25. Yang L.-X., Yang X. The spread of computer viruses under the influence of removable storage devices. Appl Math Comput 2012, 219(8):3914-3922.
26. Yang M., Zhang Z., Li Q., Zhang G. An SLBRS model with vertical transmission of computer virus over the Internet. Discrete Dyn Nat Soc 2012, 2012:1-17. (Article ID 925648).
27. Yang X., Mishra B.K., Liu Y. Computer virus: Theory, model, and methods. Discrete Dyn Nat Soc 2012, 2012:1-2. (Article ID 473508).
28. Yang X., Yang L.-X. Towards the epidemiological modeling of computer viruses. Discrete Dyn Nat Soc 2012, 2012:1-11. (Article ID 259671).
29. Yao Y., Xiang W., Qu A., Yu G., Gao F. Hopf bifurcation in an SEIDQV worm propagation model with quarantine strategy. Discrete Dyn Nat Soc 2012, 2012:1-18. (Article ID 304868).
30. Yao Y., Guo L., Guo H., Yu G., Gao F., Tong X. Pulse quarantine strategy of internet worm propagation: Modeling and analysis. Comput Electr Eng 2012, 38:1047-1061.
31. Zhang C., Zhao Y., Wu Y. An impulse model for computer viruses. Discrete Dyn Nat Soc 2012, 2012:1-13. (Article ID 259671).
32. Zhang C., Zhao Y., Wu Y., Deng S. A sochastic dynamic model of computer viruses. Discrete Dyn Nat Soc 2012, 2012:1-16. (Article ID 264874).
33. Zhu Q., Yang X., Yang L.-X., Zhang C. Optimal control of computer virus under a delayed model. Appl Math Comput 2012, 218(23):11613-11619.
34. Zhu Q., Yang X., Ren J. Modeling and analysis of the spread of computer virus. Commun Nonlinear Sci Numer Simul 2012, 17(12):5117-5124.
35. Yang L.-X., Yang X., Zhu Q., Wen L. A computer virus model with graded cure rates. Nonlinear Anal Real 2013, 14(1):414-422.
36. Yang L.-X., Yang X., Liu J., Zhu Q., Gan C. Epidemics of computer viruses: a complex-network approach. Appl Math Comput 2013, 219(16):8705-8717.
37. Gan C., Yang X., Liu W., Zhu Q., Zhang X. Propagation of computer virus under human intervention: a dynamical model. Discrete Dyn Nat Soc 2012, 2012:1-8. (Article ID 106950).
38. Heffernan J.M., Smith R.J., Wahl L.M. Perspectives on the basic reproductive ratio. JR Soc Interface 2005, 2:281-293.
39. Robinson R.C. An introduction to dynamical systems: continuous and discrete 2004, Prentice Hall.
40. http://green.wangminjie.cn/newsinfo-136730.html.
41. http://pcedu.pconline.com.cn/pingce/pingcesystem/1109/2527365all.html.
42. Arriola L, Hyman J. Forward and adjoint sensitivity analysis with applications in dynamical systems, Lecture notes in linear algebra and optimizatin; 2005.
43. Faloutsos M., Faloutsos P., Faloutsos C. On power-law relationships of the Internet topology. ACM SIGCOMM Comput Commun Rev 1999, 29(4):251-262.