The Contact Process with Switching

TL;DR

This paper introduces a generalized Contact Process allowing particles to switch types, modeling phenomena like phenotypic switching, and analyzes its properties, phase transitions, and scaling limits.

Contribution

It extends the classical Contact Process by incorporating type switching, unifies several existing models, and provides rigorous bounds and analysis of phase transitions and scaling behaviors.

Findings

Established basic properties similar to classical Contact Process.

Proved existence of phase transition through couplings.

Derived bounds and analyzed scaling limits for different switching regimes.

Abstract

In this paper, we introduce a type switching mechanism for the Contact Process on the lattice $\mathbb{Z}^d$. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the different types may exhibit specific infection and recovery dynamics. Such type switches can eg.\ be motivated from biology, where 'phenotypic switching' is common among micro-organisms. Our framework includes as special cases systems with switches between 'active' and 'dormant' states (the Contact Process with dormancy, CPD), and the Contact Process in a randomly evolving environment (CPREE) introduced by Broman (2007). The 'standard' multi-type Contact Process (without type-switching) can also be recovered as a limiting case. After constructing the process from a graphical representation, we establish several basic properties that are mostly analogous to the classical Contact Process. We then provide couplings between several variants of the system, which in particular yield the existence of a phase transition. Further, we investigate the effect of the switching parameters on the critical value of the system by providing rigorous bounds obtained from the coupling arguments as well as numerical and heuristic results. Finally, we investigate scaling limits for the process as the switching parameters tend to 0 (slow switching regime) resp.\ $\infty$ (fast switching regime). We conclude with a brief discussion of further model variants and questions for future research.