The Mutating Contact Process: Model Introduction and Qualitative Analysis of Phase Transitions in its Survival

TL;DR

This paper introduces the mutating contact process, a new variant of the multitype contact process, and analyzes its phase transitions, revealing different survival behaviors on various structures and the eventual extinction of mutants.

Contribution

The paper presents the first analysis of the mutating contact process, establishing phase transition results and survival/extinction criteria on different graph structures.

Findings

Single mutants cannot survive on $\\mathbb{Z}$.

On $\mathbb{T}_d$, there are distinct weak survival and extinction phases.

The limiting distribution favors configurations with no mutants of the first type.

Abstract

We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on $\mathbb{T}_{d}$ there are distinct weak survival and extinction of a single mutant phases, yet the limiting distribution concentrates on configurations with no mutants of the first type for any values of the parameters.