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This is a Quantitative Study study.

October 16, 2025Open Access

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

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Analysis of phase transition and infection dynamics in directed complex networks, highlighting key epidemic thresholds.

The SIS model shows a nonequilibrium phase transition at the epidemic threshold, distinguishing absorbing and endemic phases.
Critical behavior is determined by the mean degree and infection rate, with unique sensitivity to infection-rate distribution form.
Divergence of the inverse participation ratio near the epidemic threshold suggests disease localization on specific nodes.
Network heterogeneities significantly influence the dynamics of epidemic spreading across directed networks.

Müller et al. (2025) studied this question.

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