## Rare regions of the SIS model on Barabási-Albert networks    [PDF]

Géza Ódor
I extend a previous work to susceptible-infected-susceptible (SIS) models on weighed Barab\'asi-Albert scale-free trees. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder in topologies previously studied with Contact Process. I compare simulation results with a spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects and smeared phase transitions due to network inhomogeneities. Finite size study of the QMF shows the expected disappearance of the epidemic threshold $\lambda_c$ in the thermodynamic limit and suggest a nontrivial mean-field behavior characterized by the order parameter $\beta=2$. This means that the order parameter of the infection $\rho(\lambda)$ vanishes tangentially at the $\lambda_c=0$ transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths Phases as the consequence of quenched topological heterogenities.
View original: http://arxiv.org/abs/1301.4407