A novel computer virus model and its dynamics.

*(English)*Zbl 1238.34076Summary: We propose a novel computer virus propagation model and study its dynamic behaviors; to our knowledge, this is the first time the effect of anti-virus ability has been taken into account in this way. In this context, we give the threshold for determining whether the virus dies out completely. Then, we study the existence of equilibria, and analyze their local and global asymptotic stability. Next, we find that, depending on the anti-virus ability, a backward bifurcation or a Hopf bifurcation may occur. Finally, we show that under appropriate conditions, bistable states may be around. Numerical results illustrate some typical phenomena that may occur in the virus propagation over computer network.

##### MSC:

34C23 | Bifurcation theory for ordinary differential equations |

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

37N25 | Dynamical systems in biology |

34D23 | Global stability of solutions to ordinary differential equations |

68M10 | Network design and communication in computer systems |

68M11 | Internet topics |

92D30 | Epidemiology |

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\textit{J. Ren} et al., Nonlinear Anal., Real World Appl. 13, No. 1, 376--384 (2012; Zbl 1238.34076)

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