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Dynamical Analysis of a Computer Virus Propagation Model with Delay and Infectivity in Latent Period

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  • Zizhen Zhang
  • Dianjie Bi

Abstract

A delayed SLB computer virus propagation model with infectivity in latent period is proposed in this paper. We establish sufficient conditions for local stability of the positive equilibrium and existence of Hopf bifurcation by analyzing distribution of the roots of the associated characteristic equation and applying the Hopf bifurcation theorem. Furthermore, properties of the Hopf bifurcation are determined by using the normal form theory and the center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are carried out.

Suggested Citation

  • Zizhen Zhang & Dianjie Bi, 2016. "Dynamical Analysis of a Computer Virus Propagation Model with Delay and Infectivity in Latent Period," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:3067872
    DOI: 10.1155/2016/3067872
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    References listed on IDEAS

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    2. Changjin Xu & Xiaofei He, 2011. "Stability and Bifurcation Analysis in a Class of Two‐Neuron Networks with Resonant Bilinear Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Juan Liu, 2014. "Hopf Bifurcation in a Delayed SEIQRS Model for the Transmission of Malicious Objects in Computer Network," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, March.
    4. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, November.
    5. Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Juan Liu, 2014. "Hopf Bifurcation in a Delayed SEIQRS Model for the Transmission of Malicious Objects in Computer Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
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