293
Views
44
CrossRef citations to date
0
Altmetric
Section A

Global stability of a delayed SIRS computer virus propagation model

, &
Pages 347-367 | Received 12 Sep 2012, Accepted 20 Mar 2013, Published online: 20 May 2013

REFERENCES

  • J.L. Aron, M. O'Leary, R.A. Gove, S. Azadegan, and M.C. Schneider, The benefits of a notification process in addressing the worsening computer virus problem: Results of a survey and a simulation model, Comput. Secur. 21 (2002), pp. 142–163. doi: 10.1016/S0167-4048(02)00210-9
  • A. Bissett, Some human dimensions of computer virus creation and infection, Int. J. Human Comput. Stud. 52 (2000), pp. 899–913. doi: 10.1006/ijhc.1999.0361
  • F. Cohen, Computer virus: Theory and experiments, Comput. Secur. 6 (1987), pp. 22–35. doi: 10.1016/0167-4048(87)90122-2
  • Y. Enatsu, Y. Nakata, and Y. Muroya, Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model, Nonlinear Anal. RWA 13 (2012), pp. 2120–2133. doi: 10.1016/j.nonrwa.2012.01.007
  • X. Han and Q. Tan, Dynamical behavior of computer virus on internet, Appl. Math. Comput. 217 (2010), pp. 2520–2526. doi: 10.1016/j.amc.2010.07.064
  • Y.B. Kafai and S. White, Understanding virtual epidemics: Children's folk conceptions of a computer virus, J. Sci. Edu. Tech. 6 (2009), pp. 523–529.
  • J.O. Kephart and S.R. White, Measuring and modeling computer virus prevalence, 1993 IEEE Computer Society Symposium on Research in Security and Privacy: Proceedings, Oakland, CA, May 24–25, 1993, pp. 2–15.
  • J.O. Kephart, S.R. White, and D.M. Chess, Computers and epidemiology, IEEE Spectr. 30 (1993), pp. 20–26. doi: 10.1109/6.275061
  • Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, CA 1993.
  • E. Makinen, Comment on ‘A frame work for modeling trojans and computer virus infection’, Comput. J. 44 (2004), pp. 321–323. doi: 10.1093/comjnl/44.4.321
  • C.C. McCluskey, Complete global stability for an SIR epidemic model with delay – Distributed or discrete, Nonlinear Anal. RWA 11 (2010) 55–59. doi: 10.1016/j.nonrwa.2008.10.014
  • B.K. Mishra and N. Jha, Fix period of temporary immunity after run of antimalicious software on computer nodes, Appl. Math. Comput. 190 (2007), pp. 1207–1212. doi: 10.1016/j.amc.2007.02.004
  • B.K. Mishra and N. Jha, An SEIQRS model for the transmission of malicious objects in computer network, Appl. Math. Model. 34 (2010), pp. 710–715. doi: 10.1016/j.apm.2009.06.011
  • B.K. Mishra and S.K. Pandey, Dynamic model of worms with vertical transmission in computer network, Appl. Math. Model. 217 (2011), pp. 8438–8446.
  • Y. Muroya, Y. Enatsu, and Y. Nakata, Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays, Nonlinear Anal. RWA 12 (2011), pp. 1897–1910. doi: 10.1016/j.nonrwa.2010.12.002
  • W. Murray, The application of epidemiology to computer viruses, Comput. Secur. 7 (1988), pp. 139–150. doi: 10.1016/0167-4048(88)90327-6
  • R. Perdisci, A. Lanzi, and W. Lee, Classification of packed executables for accurate computer virus detection, Pattern Recognit. Lett. 29 (2008), pp. 1941–1946. doi: 10.1016/j.patrec.2008.06.016
  • J.R.C. Piqueira and V.O. Araujo, A modified epidemiological model for computer viruses, Appl. Math. Comput. 213 (2009), pp. 355–360. doi: 10.1016/j.amc.2009.03.023
  • J. Ren, X. Yang, L.-X. Yang, Y. Xu, and F. Yanga, A delayed computer virus propagation model and its dynamics, Chaos Soliton Fract. 45 (2012), pp. 74–79. doi: 10.1016/j.chaos.2011.10.003
  • J. Ren, Q. Zhu, L.-X. Yang, and C. Zhang, A novel computer virus model and its dynamics, Nonlinear Anal. RWA 13 (2012), pp. 376–384. doi: 10.1016/j.nonrwa.2011.07.048
  • X.Y. Song and L.S. Chen, Optimal harvesting and stability for a two-species competing system with stage structure, Math. Biosci. 170 (2001), pp. 173–186. doi: 10.1016/S0025-5564(00)00068-7
  • L.P. Song, Z. Jin, G.Q. Sun, J. Zhang, and X. Han, Influence of removable devices on computer worms: Dynamic analysis and control strategies, Comput. Math. Appl. Comput. Math. 61 (2011), pp. 1823–1829. doi: 10.1016/j.camwa.2011.02.010
  • J.C. Wierman and D.J. Marchette, Modeling computer virus prevalence with a susceptible–infected–susceptible model with reintroduction, Comput. Stat. Data Anal. 45 (2004), pp. 3–23. doi: 10.1016/S0167-9473(03)00113-0
  • R. Xu and Z. Ma, Stability of a delayed SIRS epidemic model with a nonlinear incidence rate, Chaos Soliton Fract. 41 (2009), pp. 2319–2325. doi: 10.1016/j.chaos.2008.09.007
  • L. Yang, X. Yang, Q. Zhu, and L. Wen, A computer virus model with graded cure rates, Nonlinear Anal. RWA 14 (2013), pp. 414–422. doi: 10.1016/j.nonrwa.2012.07.005

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.