The contact process on scale-free geometric random graphs

Peter Gracar and Arne Grauer

Stochastic Processes and their Applications, 2024, vol. 173, issue C

Abstract: We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on Rd. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.

Keywords: contact process; scale-free; exctinction; meta-stability; geometric random graph (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104360

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