2011/06/30 by Sergio Gómez, Sergio Gomez, Jesus Gomez-Gardenes +4 · 4 citations
Medicine · Physics and Astronomy · #Complex Network Analysis Techniques #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #physics.comp-ph #physics.data-an #physics.soc-ph
paper · pdf · doi:10.1103/physreve.84.036105
published as Physical Review E 84 (2011) 036105 · 7 pages
arxiv created 2011/06/30 · openalex publication_date 2011/09/09 · arxiv updated 2012/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a nonperturbative formulation of the heterogeneous mean-field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The nonperturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a nonperturbative formulation that can be solved by fixed-point iteration, and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics. Our results are in close agreement with Monte Carlo simulations, thus enhancing the predictive power of the classical heterogeneous mean-field approach, while providing a more effective framework in terms of computational time.