- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 210291, 7 pages
Optimal Control of a Delay-Varying Computer Virus Propagation Model
1College of Computer, Jiangsu Normal University, Jiangsu 221116, China
2College of Bioengineering, Chongqing University, Chongqing 400044, China
3School of Information Engineering, Guangdong Medical College, Dongguan 523808, China
Received 1 April 2013; Revised 20 July 2013; Accepted 21 July 2013
Academic Editor: Xiaofan Yang
Copyright © 2013 Jianguo Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. C. Wierman and D. J. Marchette, “Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction,” Computational Statistics & Data Analysis, vol. 45, no. 1, pp. 3–23, 2004.
- J. R. C. Piqueira and V. O. Araujo, “A modified epidemiological model for computer viruses,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 355–360, 2009.
- C. Gan, X. Yang, W. Liu, Q. Zhu, and X. Zhang, “Propagation of computer virus under human intervention: a dynamical model,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 106950, 8 pages, 2012.
- Q. Zhu, X. Yang, and J. Ren, “Modeling and analysis of the spread of computer virus,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 5117–5124, 2012.
- L.-X. Yang, X. Yang, J. Liu, Q. Zhu, and C. Gan, “Epidemics of computer viruses: s complex-network approach,” Applied Mathematics and Computation, vol. 219, no. 16, pp. 8705–8717, 2013.
- B. K. Mishra and D. K. Saini, “SEIRS epidemic model with delay for transmission of malicious objects in computer network,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1476–1482, 2007.
- B. K. Mishra and N. Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes,” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1207–1212, 2007.
- 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.
- 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.
- J. Ren, X. Yang, Q. Zhu, L.-X. Yang, and C. Zhang, “A novel computer virus model and its dynamics,” Nonlinear Analysis: Real World Applications, vol. 13, no. 1, pp. 376–384, 2012.
- J. Ren, X. Yang, L.-X. Yang, Y. Xu, and F. Yang, “A delayed computer virus propagation model and its dynamics,” Chaos, Solitons & Fractals, vol. 45, no. 1, pp. 74–79, 2012.
- 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.
- X. Yang, B. K. Mishra, and Y. Liu, “Theory, model and methods,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 473508, 2 pages, 2012.
- X. Yang and L. -X. Yang, “Towards the epidemiological modeling of computer viruses,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 259671, 11 pages, 2012.
- 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.
- J. Ren and Y. Xu, “Dynamics of a delay-varying computer virus propagation model,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 372192, 12 pages, 2012.
- C. Zhang, X. Yang, and Q. Zhu, “An optimal control model for computer viruses,” Journal of Information and Computational Science, vol. 8, no. 13, pp. 2587–2596, 2011.
- Q. Zhu and X. Yang, “Optimal control of computer virus under a delayed model,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11613–11619.
- J. Ren and X. Yang, “Dynamics and optimal shelter for computer virus propagation in network,” Journal of Information and Computational Science, vol. 8, no. 9, pp. 1735–1745, 2011.
- D. Moore, C. Shannon, G. M. Voelker, and S. Savage, “Internet quarantine: requirements for containing self-propagating code,” in Proceedings of the 22nd IEEE Annual Joint Conference on the Computer and Communications Societies (INFOCOM '03), pp. 1901–1910, IEEE, April 2003.
- T. M. Chen and N. Jamil, “Effectiveness of quarantine in worm epidemics,” in Proceedings of the IEEE International Conference on Communications (ICC '05), pp. 2142–2147, IEEE, July 2005.
- W. H. Fleming and R. W. Rishel, Deterministic and Stochastic, Springer, Berlin, Germany, 1975.
- D. L. Lukes, Differential Equations: Classical to Controlled, vol. 162 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1982.
- M. L. Kamien and N. L. Schwartz, Dynamics Optimization: The Clculus of Variations and Optimal Control in Economics and Management, Elsevier Science, Amsterdam, The Netherlands, 2000.