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**Hopf bifurcation analysis of a delayed viral infection model in computer networks.**
*(English)*
Zbl 1255.34071

Summary: A novel computer virus propagation model with dual delays and multi-state antivirus measures is considered. Using theories of stability and bifurcation, it is proven that there exists a critical value of delay for the stability of virus prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the explicit formulas determining the stability and direction of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to verify the theoretical analysis. The conclusions of this paper can contribute to a better theoretical basis for understanding the long-term actions of virus propagation in networks.

### MSC:

34K18 | Bifurcation theory of functional-differential equations |

68M10 | Network design and communication in computer systems |

68M11 | Internet topics |

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\textit{L. Feng} et al., Math. Comput. Modelling 56, No. 7--8, 167--179 (2012; Zbl 1255.34071)

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