Epidemics on critical random graphs with heavy-tailed degree distribution

David Clancy

Stochastic Processes and their Applications, 2025, vol. 179, issue C

Abstract: We study the susceptible–infected–recovered (SIR) epidemic on a random graph chosen uniformly over all graphs with certain critical, heavy-tailed degree distributions. We prove process level scaling limits for the number of individuals infected on day h on the largest connected components of the graph. The scaling limits contain non-negative jumps corresponding to some vertices of large degree. These weak convergence techniques allow us to describe the height profile of the α-stable continuum random graph (Goldschmidt et al., 2022; Conchon-Kerjan and Goldschmidt, 2023), extending results known in the Brownian case (Miermont and Sen, 2022). We also prove model-independent results that can be used on other critical random graph models.

Keywords: Configuration model; Stable excursions; Random graphs; Lamperti transform; SIR model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104510

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