TY - ELEC
AU - Silvio C. Ferreira
PY - 2019
TI - Eigenvector localization, dynamical correlations and epidemic thresholds on random networks with degree correlations
LA - eng
M3 - Moving Image
AB - I will present comparisons between large-scale stochastic simulations and
mean-field theories for the epidemic thresholds and prevalence of the
susceptible-infected-susceptible (SIS) model on networks with power-law degree
distributions and degree correlations. We confirm the vanishing of the threshold
regardless of the correlation pattern and degree exponent. The thresholds are
compared with heterogeneous mean-field (HMF), quenched mean-field (QMF) and
pair quenched mean-field (PQMF) theories where the degree correlation patterns
are explicitly considered. The PQMF, which additionally reckons dynamical correlations,
outperforms the other two theories and its level of quantitative success
depends on the type of degree correlation (assortative, disassortative or
uncorrelated). Furthermore, we observe a strong correlation between the success
of PQMF theory and the properties of the principal eigenvector such as the
inverse participation ration (IPR) and the spectral gap. If the IPR is large and
tends to a finite value at the limit of large networks the PQMF predictions
deviate from numerical simulations. Otherwise, if the IPR is small, PQMF theory
shows an excellent match with the simulations. Finally, the epidemic prevalence
near to the critical point and the corresponding critical exponents are compared
with both QMF theory and exact results.
N2 - I will present comparisons between large-scale stochastic simulations and
mean-field theories for the epidemic thresholds and prevalence of the
susceptible-infected-susceptible (SIS) model on networks with power-law degree
distributions and degree correlations. We confirm the vanishing of the threshold
regardless of the correlation pattern and degree exponent. The thresholds are
compared with heterogeneous mean-field (HMF), quenched mean-field (QMF) and
pair quenched mean-field (PQMF) theories where the degree correlation patterns
are explicitly considered. The PQMF, which additionally reckons dynamical correlations,
outperforms the other two theories and its level of quantitative success
depends on the type of degree correlation (assortative, disassortative or
uncorrelated). Furthermore, we observe a strong correlation between the success
of PQMF theory and the properties of the principal eigenvector such as the
inverse participation ration (IPR) and the spectral gap. If the IPR is large and
tends to a finite value at the limit of large networks the PQMF predictions
deviate from numerical simulations. Otherwise, if the IPR is small, PQMF theory
shows an excellent match with the simulations. Finally, the epidemic prevalence
near to the critical point and the corresponding critical exponents are compared
with both QMF theory and exact results.
UR - https://open.library.ubc.ca/collections/48630/items/1.0385522
ER - End of Reference