Survival and coexistence for a multitype contact process

TL;DR

This paper investigates the conditions for coexistence and convergence in a multitype contact process, revealing differences between lattice and tree structures and identifying parameter regimes for stable coexistence.

Contribution

It provides new theoretical results on coexistence and convergence in multitype contact processes on different graph structures, extending previous understanding.

Findings

Coexistence occurs on trees within a specific birth rate interval.

Complete convergence is established outside this interval.

Differences between lattice and tree structures are characterized.

Abstract

We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the $d$-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.