Spread of infections in a heterogeneous moving population

Duncan Alexander McNicol Dauvergne, Allan Sly

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider a model where an infection moves through a collection of particles performing independent random walks. In this model, Kesten and Sidoravicius established linear growth of the infected region when infected and susceptible particles move at the same speed. In this paper we establish a linear growth rate when infected and susceptible particles move at different speeds, answering an open problem from their work. Our proof combines an intricate coupling of Poisson processes with a streamlined version of a percolation model of Sidoravicius and Stauffer.

Original languageEnglish (US)
Pages (from-to)73-131
Number of pages59
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Oct 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Growth model
  • Infection spread
  • Interacting particle systems
  • Random walks


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