SURVIVAL AND EXTINCTION OF EPIDEMICS ON RANDOM GRAPHS WITH GENERAL DEGREE

Shankar Bhamidi, Danny Nam, Oanh Thi Hoang Nguyen, Allan Sly

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper we establish the necessary and sufficient criterion for the contact process on Galton–Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short survival). We prove that the survival threshold λ 1 for a Galton–Watson tree is strictly positive if and only if its offspring distribution ξ has an exponential tail, that is, E e<∞ for some c> 0, settling a conjecture by Huang and Durrett (2018). On the random graph with degree distribution μ, we show that if μ has an exponential tail, then for small enough λ the contact process with the all-infected initial condition survives for n 1+ o( 1 )-time whp (short survival), while for large enough λ it runs over e①(n)-time whp (long survival). When μ is subexponential, we prove that the contact process whp displays long survival for any fixed λ> 0.

Original languageEnglish (US)
Pages (from-to)244-286
Number of pages43
JournalAnnals of Probability
Volume49
Issue number1
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Contact process
  • epidemics
  • Galton–Watson tree
  • phase transition
  • random graph

Fingerprint

Dive into the research topics of 'SURVIVAL AND EXTINCTION OF EPIDEMICS ON RANDOM GRAPHS WITH GENERAL DEGREE'. Together they form a unique fingerprint.

Cite this