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A delayed computer virus propagation model and its dynamics

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  • Ren, Jianguo
  • Yang, Xiaofan
  • Yang, Lu-Xing
  • Xu, Yonghong
  • Yang, Fanzhou

Abstract

In this paper, we propose a delayed computer virus propagation model and study its dynamic behaviors. First, we give the threshold value R0 determining whether the virus dies out completely. Second, we study the local asymptotic stability of the equilibria of this model and it is found that, depending on the time delays, a Hopf bifurcation may occur in the model. Next, we prove that, if R0=1, the virus-free equilibrium is globally attractive; and when R0<1, it is globally asymptotically stable. Finally, a sufficient criterion for the global stability of the virus equilibrium is obtained.

Suggested Citation

  • Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:1:p:74-79
    DOI: 10.1016/j.chaos.2011.10.003
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Negi, Kuldeep, 2008. "Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 626-638.
    2. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    3. Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    4. Li, Xue-Zhi & Zhou, Lin-Lin, 2009. "Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 874-884.
    5. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    6. Wierman, John C. & Marchette, David J., 2004. "Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 3-23, February.
    7. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
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    Cited by:

    1. Zizhen Zhang & Soumen Kundu & Ruibin Wei, 2019. "A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    2. Chen, Lijuan & Hattaf, Khalid & Sun, Jitao, 2015. "Optimal control of a delayed SLBS computer virus model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 244-250.
    3. Yonghong Xu & Jianguo Ren, 2016. "Propagation Effect of a Virus Outbreak on a Network with Limited Anti-Virus Ability," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    4. Piqueira, José Roberto C. & Cabrera, Manuel A.M. & Batistela, Cristiane M., 2021. "Malware propagation in clustered computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    5. Chenquan Gan & Xiaofan Yang & Wanping Liu & Qingyi Zhu & Xulong Zhang, 2012. "Propagation of Computer Virus under Human Intervention: A Dynamical Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-8, July.
    6. Yang, Lu-Xing & Draief, Moez & Yang, Xiaofan, 2016. "The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 403-415.
    7. Wei Yang, 2021. "Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay," Dynamic Games and Applications, Springer, vol. 11(4), pages 892-914, December.
    8. Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2020. "A hybrid analytical scheme for the numerical computation of time fractional computer virus propagation model and its stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    9. Yang, Lu-Xing & Yang, Xiaofan, 2013. "The effect of infected external computers on the spread of viruses: A compartment modeling study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6523-6535.
    10. Hu, Zhixing & Wang, Hongwei & Liao, Fucheng & Ma, Wanbiao, 2015. "Stability analysis of a computer virus model in latent period," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 20-28.
    11. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    12. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    13. Yang, Lu-Xing & Yang, Xiaofan, 2014. "The spread of computer viruses over a reduced scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 173-184.
    14. Zhang, Chunming & Huang, Haitao, 2016. "Optimal control strategy for a novel computer virus propagation model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 251-265.
    15. Zizhen Zhang & Huizhong Yang, 2015. "Hopf Bifurcation of an SIQR Computer Virus Model with Time Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, January.
    16. Hu Zhang & Anwar Zeb & Aying Wan & Zizhen Zhang, 2022. "Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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