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The contact process on scale-free networks evolving by vertex updating
Emmanuel Jacob1, Peter Mörters2
1Unité de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, Lyon, France.
Royal Society Open Science
|June 3, 2017
Summary
This study proves a phase transition in evolving scale-free networks for the contact process. Temporal network variability accelerates spread and shortens metastable states, unlike static networks.
Area of Science:
- Network science
- Epidemiology
- Statistical physics
Background:
- The contact process models disease spread on networks.
- Scale-free networks exhibit heterogeneous connectivity.
- Dynamic network changes can impact epidemic dynamics.
Purpose of the Study:
- To rigorously investigate the contact process on evolving scale-free networks.
- To identify and characterize phase transitions in epidemic survival.
- To compare dynamics with static networks and mean-field approximations.
Main Methods:
- Mathematical proof of phase transition.
- Analysis of infection survival time (exponential vs. polynomial).
- Comparison of power-law exponent thresholds.
Main Results:
- A phase transition occurs at a power-law exponent of four.
- Evolving networks show a transition absent in static counterparts.
- Temporal variability enhances spread and reduces metastable state durations.
Conclusions:
- Network evolution introduces a critical exponent for epidemic survival.
- Dynamic network properties are crucial for understanding disease dynamics.
- Temporal variability offers a novel mechanism influencing epidemic outcomes.
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