2025/08/08 by Vinícius B. Müller, Fernando L. Metz, Müller, Vinícius B. +1 · 1 citation
Physics and Astronomy · Psychology · #Complex Network Analysis Techniques #Mental Health Research Topics
paper · pdf · doi:10.48550/arxiv.2508.06332
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 ≥ λ-1, where c is the mean degree and λ 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.