Chase-escape with conversion as a multiple sclerosis lesion model

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.