Spread of infections in a heterogeneous moving population

TL;DR

This paper extends the understanding of infection spread in a moving population by proving linear growth rates even when infected and susceptible particles move at different speeds, using advanced probabilistic coupling methods.

Contribution

It establishes a linear growth rate of infection spread for particles moving at different speeds, solving an open problem from prior research.

Findings

Linear growth of infected region when particles move at different speeds

Novel coupling of Poisson processes with percolation models

Answers an open problem from Kesten and Sidoravicius' work

Abstract

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.