On the Optimal Dynamic Control Strategy of Disruptive Computer Virus

Discrete Dynamics in Nature and Society

Volumn 2017, Issue , 2017, Pages

  Bi, Jichao ^a   Yang, Xiaofan ^a   Wu, Yingbo ^a   Xiong, Qingyu ^a   Wen, Junhao ^a   Tang, Yuan Yan ^b  

^a CHONGQING UNIVERSITY   (China)

^b UNIVERSITY OF MACAU   (Macao)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85017163701     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2017/8390784     Document Type: Article

References (61)

1. P. Szor, The Art of Computer Virus Research and Defense, Addison-Wesley Education Publishers, 2005.
2. Y.Wang, S.Wen, Y. Xiang, andW. Zhou, "Modeling the propagation of worms in networks: a survey," IEEE Communications Surveys and Tutorials, vol. 16, no. 2, pp. 942-960, 2014.
3. J. O. Kephart and S. R. White, "Directed-graph epidemiological models of computer viruses," in Proceedings of the IEEE Computer Society Symposium on Research in Security and Privacy, pp. 343-359, Oakland, Calif, USA, May 1991.
4. J. O. Kephart and S. R. White, "Measuring and modeling computer virus prevalence," in Proceedings of the IEEE Computer Society Symposiumon Research in Security and Privacy, pp. 2-15, Oakland, Calif, USA, May 1993.
5. J. R. Piqueira and V. O. Araujo, "A modified epidemiological model for computer viruses," AppliedMathematics and Computation, vol. 213, no. 2, pp. 355-360, 2009.
6. B. K.Mishra and S. K. Pandey, "Dynamic model of worms with vertical transmission in computer network," AppliedMathematics and Computation, vol. 217, no. 21, pp. 8438-8446, 2011.
7. Y. Yao, W. Xiang, A. Qu, G. Yu, and F. Gao, "Hopf bifurcation in an SEIDQV worm propagation model with quarantine strategy," Discrete Dynamics in Nature and Society, vol. 2012, Article ID 304868, 18 pages, 2012.
8. L. Feng, X.Liao, Q. Han, andL. Song, "Modeling and analysis of peer-to-peer botnets," Discrete Dynamics in Nature and Society, vol. 2012, Article ID865075, 18 pages, 2012.
9. Y. Li, J. Pan, L. Song, and Z. Jin, "The influence of user protection behaviors on the control of internet worm propagation," Abstract and Applied Analysis, vol. 2013, Article ID 531781, 13 pages, 2013.
10. Y. Yao, X.-W. Xie, H. Guo, G. Yu, F.-X. Gao, and X.-J. Tong, "Hopf bifurcation in an Internet worm propagation model with time delay in quarantine," Mathematical and Computer Modelling, vol. 57, no. 11-12, pp. 2635-2646, 2013.
11. Y. Muroya, Y. Enatsu, and H. Li, "Global stability of a delayed SIRS computer virus propagation model," International Journal of Computer Mathematics, vol. 91, no. 3, pp. 347-367, 2014.
12. Z. Zhang and H. Yang, "Hopf bifurcation of an SIQR computer virus model with time delay," Discrete Dynamics in Nature and Society, vol. 2015, Article ID 101874, 8 pages, 2015.
13. R. Pastor-Satorras and A. Vespignani, "Epidemic spreading in scale-free networks," Physical Review Letters, vol. 86, no. 14, pp. 3200-3203, 2001.
14. M. Barthelemy, A. Barrat,R. Pastor-Satorras, and A.Vespignani, "Velocity and hierarchical spread of epidemic outbreaks in scale-free networks," Physical Review Letters, vol. 92, no. 17, Article ID 178701, 2004.
15. M. Yang, G. Chen, and X. Fu, "A modified SIS model with an infective medium on complex networks and its global stability," PhysicaA: StatisticalMechanics and ItsApplications, vol. 390, no. 12, pp. 2408-2413, 2011.
16. J. Ren, Y. Xu, and J. Liu, "Investigation of dynamics of a virusantivirus model in complex network," Physica A: Statistical Mechanics and its Applications, vol. 421, pp. 533-540, 2015.
17. J. Ren, J. Liu, and Y. Xu, "Modeling the dynamics of a networkbased model of virus attacks on targeted resources," Communications in Nonlinear Science and Numerical Simulation, vol. 31, no. 1-3, pp. 1-10, 2016.
18. P. Van Mieghem, J. Omic, and R. Kooij, "Virus spread in networks," IEEE/ACM Transactions on Networking, vol. 17, no. 1, pp. 1-14, 2009.
19. P. Van Mieghem, "The N-intertwined SIS epidemic network model," Computing, vol. 93, no. 2, pp. 147-169, 2011.
20. S. Xu, W. Lu, and Z. Zhan, "A stochastic model of multivirus dynamics," IEEE Transactions on Dependable and Secure Computing, vol. 9, no. 1, pp. 30-45, 2012.
21. F. D. Sahneh, F. N. Chowdhury, and C. M. Scoglio, "On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading," Scientific Reports, vol. 2, article 632, 2012.
22. P. Van Mieghem, "Approximate formula and bounds for the time-varying susceptible-infected-susceptible prevalence in networks," Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, vol. 93, no. 5, Article ID052312, 2016.
23. C. Nowzari, V. M. Preciado, and G. J. Pappas, "Analysis and control of epidemics: a survey of spreading processes on complex networks," IEEE Control Systems, vol. 36, no. 1, pp. 26-46, 2016.
24. V. M. Preciado, F. D. Sahneh, and C. Scoglio, "A convex framework for optimal investment on disease awareness in social networks," in Proceedings of the 1st IEEE Global Conference on Signal and Information Processing (GlobalSIP '13), pp. 851-854, Austin, Tex, USA, December 2013.
25. V. M. Preciado, M. Zargham, C. Enyioha, A. Jadbabaie, and G. J. Pappas, "Optimal resource allocation for network protection against spreading processes," IEEE Transactions on Control of Network Systems, vol. 1, no. 1, pp. 99-108, 2014.
26. C. Nowzari, M. Ogura, V. M. Preciado, and G. J. Pappas, "Optimal resource allocation for containing epidemics on time-varying networks," in Proceedings of the 49th Asilomar Conference on Signals, Systems and Computers (ACSSC '15), pp. 1333-1337, Pacific Grove, Calif, USA, November 2015.
27. H. Shakeri, F. D. Sahneh, C. Scoglio, P. Poggi-Corradini, and V. M. Preciado, "Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks," Mathematical Biosciences and Engineering. MBE, vol. 12, no. 3, pp. 609-623, 2015.
28. N. J. Watkins, C. Nowzari, V. M. Preciado, and G. J. Pappas, "Optimal resource allocation for competitive spreading processes on bilayer networks," IEEE Transactions on Control of Network Systems, 2016.
29. E. Hansen and T. Day, "Optimal control of epidemics with limited resources," Journal of Mathematical Biology, vol. 62, no. 3, pp. 423-451, 2011.
30. M. H. R. Khouzani, S. Sarkar, and E. Altman, "Optimal dissemination of security patches in mobile wireless networks," IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4714-4732, 2012.
31. S. Eshghi, M. H. R. Khouzani, S. Sarkar, and S. S. Venkatesh, "Optimal patching in clustered malware epidemics," IEEE/ACM Transactions on Networking, vol. 24, no. 1, pp. 283-298, 2016.
32. A. Khanafer and T. Basar, "An optimal control problem over infected networks," in Proceedings of the International Conference of Control, Dynamic Systems, and Robotics, Ottawa, Canada, May 2014.
33. L.-X. Yang, M. Draief, and X. Yang, "The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model," Physica A. Statistical Mechanics and Its Applications, vol. 450, pp. 403-415, 2016.
34. L.-X. Yang and X. Yang, "Propagation behavior of virus codes in the situation that infected computers are connected to the internet with positive probability," Discrete Dynamics in Nature and Society, vol. 2012, Article ID 693695, 13 pages, 2012.
35. L.-X. Yang and X. Yang, "The spread of computer viruses under the influence of removable storage devices," Applied Mathematics and Computation, vol. 219, no. 8, pp. 3914-3922, 2012.
36. L.-X. Yang, X. Yang, L.Wen, and J. Liu, "A novel computer virus propagation model and its dynamics," International Journal of Computer Mathematics, vol. 89, no. 17, pp. 2307-2314, 2012.
37. L.-X. Yang, X. Yang, Q. Zhu, and L. Wen, "A computer virus model with graded cure rates," Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 414-422, 2013.
38. Y. Muroya and T. Kuniya, "Global stability of nonresident computer virus models," Mathematical Methods in the Applied Sciences, vol. 38, no. 2, pp. 281-295, 2015.
39. M. Yang, Z. Zhang, Q. Li, and G. Zhang, "An SLBRS model with vertical transmission of computer virus over the Internet," Discrete Dynamics in Nature and Society, vol. 2012, Article ID 925648, 17 pages, 2012.
40. L.-X. Yang, X. Yang, J. Liu, Q. Zhu, and C. Gan, "Epidemics of computer viruses: a complex-network approach," Applied Mathematics and Computation, vol. 219, no. 16, pp. 8705-8717, 2013.
41. L.-X. Yang and X. Yang, "A new epidemic model of computer viruses," Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 6, pp. 1935-1944, 2014.
42. C. Zhang, W. Liu, J. Xiao, and Y. Zhao, "Hopf bifurcation of an improved SLBS model under the influence of latent period," Mathematical Problems in Engineering, vol. 2013, Article ID 196214, 10 pages, 2013.
43. L.-X. Yang and X. Yang, "The impact of nonlinear infection rate on the spread of computer virus," Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, vol. 82, no. 1-2, pp. 85-95, 2015.
44. L. Chen, K. Hattaf, and J. Sun, "Optimal control of a delayed SLBS computer virus model," Physica A. Statistical Mechanics and Its Applications, vol. 427, pp. 244-250, 2015.
45. L.-X. Yang, M. Draief, and X. Yang, "The impact of the network topology on the viral prevalence: a node-based approach," PLoS ONE, vol. 10, no. 7, Article IDe0134507, 2015.
46. D. Liberzon, Calculus of Variations and Optimal ControlTheory, Princeton University Press, Princeton, NJ, USA, 2012.
47. R. C. Robinson, An Introduction to Dynamical Systems: Continuous and Discrete, Pearson Prentice Hall, Upper Saddle River, NJ, USA, 2005.
48. A.-L. Barabási and R. Albert, "Emergence of scaling in random networks," Science, vol. 286, no. 5439, pp. 509-512, 1999.
49. D. J. Watts and S. H. Strogatz, "Collective dynamics of 'smallworld' networks," Nature, vol. 393, no. 6684, pp. 440-442, 1998.
50. https://snap.stanford.edu/data/egonets-Facebook.html.
51. Y. Yao, L. Guo, H. Guo, G. Yu, F.-X. Gao, and X.-J. Tong, "Pulse quarantine strategy of internet worm propagation: modeling and analysis," Computers and Electrical Engineering, vol. 38, no. 5, pp. 1047-1061, 2012.
52. Y. Yao, X. Feng, W. Yang, W. Xiang, and F. Gao, "Analysis of a delayed Internet worm propagation model with impulsive quarantine strategy,"Mathematical Problems in Engineering, vol. 2014, Article ID369360, 18 pages, 2014.
53. T. Britton, "Stochastic epidemic models: a survey," Mathematical Biosciences, vol. 225, no. 1, pp. 24-35, 2010.
54. J. Amador and J. R. Artalejo, "Stochastic modeling of computer virus spreading with warning signals," Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 350, no. 5, pp. 1112-1138, 2013.
55. J. Amador, "The stochastic SIRA model for computer viruses," Applied Mathematics and Computation, vol. 232, pp. 1112-1124, 2014.
56. Y. Schwarzkopf, A. Rakos, and D.Mukamel, "Epidemic spreading in evolving networks," Physical Review E, vol. 82, no. 3, pp. 336-354, 2010.
57. E. Valdano, L. Ferreri, C. Poletto, and V. Colizza, "Analytical computation of the epidemic threshold on temporal networks," Physical Review X, vol. 5, no. 2, Article ID 021005, 2015.
58. M. Ogura and V. M. Preciado, "Stability of spreading processes over time-varying large-scale networks," IEEE Transactions on Network Science and Engineering, vol. 3, no. 1, pp. 44-57, 2016.
59. J. R. Piqueira, "Rumor propagation model: An Equilibrium Study,"Mathematical Problems in Engineering, vol. 2010,Article ID 631357, 7 pages, 2010.
60. S. Nizamani, N.Memon, and S. Galam, "Frompublic outrage to the burst of public violence: an epidemic-likemodel," Physica A: Statistical Mechanics and ItsApplications, vol. 416, pp. 620-630, 2014.
61. J. Xu, M. Zhang, and J. Ni, "A coupled model for government communication and rumor spreading in emergencies," Advances in Difference Equations, vol. 2016, article 208, 2016.