Epidemic thresholds of the susceptible-infected-susceptible model on networks: A comparison of numerical and theoretical results

2012/06/30 by Silvio C. Ferreira, Claudio Castellano, Romualdo Pastor‐Satorras +1 · 292 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #COVID-19 epidemiological studies #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Epidemic model #Exponent #Field (mathematics) #Geometry #Mathematics #Mean field theory #Opinion Dynamics and Social Influence #Physics #Population #Position (finance) #Quantum mechanics #Scale (ratio) #Scaling #Statistical physics #Work (physics) #cond-mat.stat-mech #cs.SI #physics.soc-ph

paper · pdf · doi:10.1103/physreve.86.041125

published in Physical Review E 86(4), 041125 (American Physical Society) · 9 pages, 8 figures, final version as in PRE

openalex publication_date 2012/10/15 · arxiv created 2012/10/16 · arxiv updated 2012/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infected-susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.

Citations

• Discrete-time Markov chain approach to contact-based disease spreading in complex networks
• Epidemic Spreading in Scale-Free Networks
• Cut-offs and finite size effects in scale-free networks
• Statistical mechanics of complex networks
• Evolution of networks

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