Spread of infections in a heterogeneous moving population

• 成果类型: Article; Early Access
• 署名作者: Dauvergne, Duncan; Sly, Allan
• 署名单位: University of Toronto; Princeton University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01216-6
• 发表日期: 2023
• 关键词: one-dimensional model; x plus y; shape theorem; fluctuations; front

摘要

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.