Distance-dependent chase-escape on trees

TL;DR

This paper establishes a precise condition for species coexistence in a parasite-host model on infinite trees, where the rates depend on the distance to the nearest parasite, highlighting the importance of spatially dependent interactions.

Contribution

It introduces a novel distance-dependent model for parasite-host interactions on trees and provides a necessary and sufficient condition for coexistence.

Findings

Derived a condition for species coexistence based on distance-dependent rates.

Showed how spatial dependence influences parasite-host dynamics.

Extended understanding of growth processes on infinite trees.

Abstract

We give a necessary and sufficient condition for species coexistence in a parasite-host growth process on infinite $d$-ary trees. The novelty of this work is that the spreading and death rates for hosts depend on the distance to the nearest parasite.