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Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software

Author

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  • Zizhen Zhang
  • Ranjit Kumar Upadhyay
  • Dianjie Bi
  • Ruibin Wei

Abstract

In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system.

Suggested Citation

  • Zizhen Zhang & Ranjit Kumar Upadhyay & Dianjie Bi & Ruibin Wei, 2018. "Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-18, November.
    • Handle: RePEc:hin:jnddns:8239823
    DOI: 10.1155/2018/8239823
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