Spread of an infection on the zero range process

TL;DR

This paper analyzes how an infection spreads in a moving population modeled by a zero range process, proving the infection front advances with positive finite velocity and establishing a space-time decoupling property.

Contribution

It introduces a novel analysis of infection spread on a zero range process, including a proof of finite velocity of the infection front and a space-time decoupling result.

Findings

Infection front moves with positive finite velocity.

Established space-time decoupling for zero range process.

Derived correlation estimates using sprinkling technique.

Abstract

We study the spread of an infection on top of a moving population. The environment evolves as a zero range process on the integer lattice starting in equilibrium. At time zero, the set of infected particles is composed by those which are on the negative axis, while particles at the right of the origin are considered healthy. A healthy particle immediately becomes infected if it shares a site with an infected particle. We prove that the front of the infection wave travels to the right with positive and finite velocity. As a central step in the proof of these results, we prove a space-time decoupling for the zero range process which is interesting on its own. Using a sprinkling technique, we derive an estimate on the correlation of functions of the space of trajectories whose supports are sufficiently far away.