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Localization transition, Lifschitz tails, and rare-region effects in network models
1Research Center for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
Summary
This study investigates how network heterogeneity impacts disease spread models. It reveals that quenched mean-field theory accurately predicts Griffiths phases and localization transitions in various network types.
Area of Science:
- Epidemiology
- Network Science
- Statistical Physics
Background:
- Heterogeneity in networks significantly influences epidemic dynamics.
- Understanding localization phenomena is crucial for disease modeling.
Purpose of the Study:
- To investigate the effects of network heterogeneity on the Susceptible-Infected-Susceptible (SIS) model.
- To analyze the emergence of localization and Griffiths phases using quenched mean-field theory.
Main Methods:
- Quenched mean-field theory application.
- Analysis of inverse participation ratio distributions.
- Comparison with simulation results and Lifshitz tails.
Main Results:
- Localization phenomena are accurately described by the inverse participation ratio.
- Griffiths phases are correctly predicted on 1D lattices and small-world networks.
- Localization transitions on scale-free networks at a specific degree exponent (γ=3) are discussed.
Conclusions:
- Quenched mean-field theory provides a robust framework for studying epidemic models with network heterogeneity.
- The findings offer insights into disease spread dynamics and phase transitions in complex systems.
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