### Abstract

Original language | English |
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Article number | 170081 |

Journal | Royal Society Open Science |

Volume | May 2017 |

DOIs | |

Publication status | Published - 24 May 2017 |

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### Cite this

*Royal Society Open Science*,

*May 2017*, [170081]. https://doi.org/10.1098/rsos.170081

**The contact process on scale-free networks evolving by vertex updating.** / Jacob, Emmanuel; Morters, Peter.

Research output: Contribution to journal › Article

*Royal Society Open Science*, vol. May 2017, 170081. https://doi.org/10.1098/rsos.170081

}

TY - JOUR

T1 - The contact process on scale-free networks evolving by vertex updating

AU - Jacob, Emmanuel

AU - Morters, Peter

PY - 2017/5/24

Y1 - 2017/5/24

N2 - We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most polynomially in the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast with that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time at which the infection spends in metastable states.

AB - We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most polynomially in the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast with that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time at which the infection spends in metastable states.

UR - https://doi.org/10.1098/rsos.170081

U2 - 10.1098/rsos.170081

DO - 10.1098/rsos.170081

M3 - Article

VL - May 2017

JO - Royal Society Open Science

JF - Royal Society Open Science

SN - 2054-5703

M1 - 170081

ER -