Switchover phenomenon for general graphs

• DOI: 10.1002/jgt.23184
• Publication Date: 2024-10-08T16:53:03Z
• Authors: Dániel Keliger; László Lovász; Tamás Ferenc Móri; Gergely Ódor
• Keywords: Switchover; Phenomenon

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) are distributed uniformly. Previously, Ódor et al. demonstrated few random graph models that expectation of total number undergoes switchover phenomenon; is more dangerous for small infection rates, while large uniform seeding expected to infect nodes. rigorously prove this claim under mild, deterministic assumptions underlying graph. If we further assume has enough expansion, second moment degree distribution bounded comparable vertices, difference between scenarios shown be macroscopic.