Epidemic threshold and localization of the SIS model on directed complex networks

Abstract

We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic approach to the distribution of fixed-point infection probabilities, we derive the phase diagram and show that the model exhibits a nonequilibrium phase transition between the absorbing and endemic phases for $c\ge {\lambda }^{-1}$, where $c$ is the mean degree and $\lambda$ the average infection rate. Interestingly, the critical line is independent of the degree distribution but is highly sensitive to the form of the infection-rate distribution. We further show that the inverse participation ratio of infection probabilities diverges near the epidemic threshold, indicating that the disease may become localized on a small fraction of nodes. These results provide a systematic characterization of how network heterogeneities shape epidemic spreading on directed contact networks within the quenched mean-field approximation.

13 pages, 9 figures

References in corpus (6)

• Thresholds for epidemic spreading in networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• On the localization transition in symmetric random matrices
• Dynamic message-passing equations for models with unidirectional dynamics
• Emergence of the giant weak-component in directed random graphs with arbitrary degree distributions
• Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure