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Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

Author

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  • Tao Dong
  • Xiaofeng Liao
  • Huaqing Li

Abstract

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

Suggested Citation

  • Tao Dong & Xiaofeng Liao & Huaqing Li, 2012. "Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, April.
    • Handle: RePEc:hin:jnlaaa:841987
    DOI: 10.1155/2012/841987
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    Cited by:

    1. 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.
    2. 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.

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