Chase-escape with conversion as a multiple sclerosis lesion model

Emma Bailey; Erin Beckman; Saraí Hernández-Torres; Matthew Junge; Aanjaneya Kumar; Ann Lee; Danny Li; tahda queer; Alisher Raufov; Lily Reeves; Omer Rondel

arXiv · 2507.21235

Chase-escape with conversion as a multiple sclerosis lesion model

Emma Bailey·Erin Beckman·Saraí Hernández-Torres·Matthew Junge·Aanjaneya Kumar·Ann Lee·Danny Li·tahda queer·Alisher Raufov·Lily Reeves·Omer Rondel

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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.

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Emma Bailey, Erin Beckman, Saraí Hernández-Torres, Matthew Junge, Aanjaneya Kumar, Ann Lee, Danny Li, tahda queer, Alisher Raufov, Lily Reeves, Omer Rondel. 2025-07-28. Chase-escape with conversion as a multiple sclerosis lesion model. https://arxiv.org/abs/2507.21235

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