Chase-escape with conversion as a multiple sclerosis lesion model

TL;DR

This paper introduces a novel stochastic chase-escape model with conversion to simulate inflammatory damage in multiple sclerosis, providing mathematical proofs of damage monotonicity and phase transition behavior on various graph structures.

Contribution

It extends the chase-escape process with conversion, offering new theoretical insights and proofs relevant to modeling multiple sclerosis damage.

Findings

Proves damage monotonicity on integers, trees, stars, and complete graphs.

Establishes phase transition existence and order on bounded degree graphs.

Provides mathematical foundation for inflammatory damage modeling.

Abstract

We introduce conversion to the stochastic process known as chase-escape in an effort to model aspects of inflammatory damage from multiple sclerosis. We prove monotonicity results for aggregate damage for the model on the positive integers, trees, stars, and the complete graph. Additionally, we establish the existence and asymptotic order of a phase transition on bounded degree graphs with a non-trivial site percolation threshold.