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Switchover phenomenon for general graphs
Title / Series / Name
Journal of Graph Theory
Publication Volume
108
Publication Issue
3
Pages
Editors
Keywords
SIR-type epidemics
graph percolation
switchover phenomenon
Geometry and Topology
Discrete Mathematics and Combinatorics
graph percolation
switchover phenomenon
Geometry and Topology
Discrete Mathematics and Combinatorics
Files
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Odor-Gergely_2025.pdf
Adobe PDF, 653.69 KB
URI
https://hdl.handle.net/20.500.14018/27882
Abstract
We study SIR‐type epidemics (susceptible‐infected‐resistant) on graphs in two scenarios: (i) when the initial infections start from a well‐connected central region and (ii) when initial infections are distributed uniformly. Previously, Ódor et al. demonstrated on a few random graph models that the expectation of the total number of infections undergoes a switchover phenomenon; the central region is more dangerous for small infection rates, while for large rates, the uniform seeding is expected to infect more nodes. We rigorously prove this claim under mild, deterministic assumptions on the underlying graph. If we further assume that the central region has a large enough expansion, the second moment of the degree distribution is bounded and the number of initial infections is comparable to the number of vertices, the difference between the two scenarios is shown to be macroscopic.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2025-10-08
Language
ISBN
Identifiers
10.1002/jgt.23184