Chase-escape with conversion as a multiple sclerosis lesion model

2025/07/28 by Bailey, Emma, Beckman, Erin, Hernández-Torres, Saraí +8 · 1 citation
#60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.21235

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.

Citations

• Phase Transition for the Chase-Escape Model on 2D Lattices
• Coexistence in chase-escape
• On the birth-and-assassination process, with an application to scotching a rumor in a network

Cited by

• Chase-escape with conversion on the complete graph

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• Chase-escape with conversion on the complete graph
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• Phase Transition for the Chase-Escape Model on 2D Lattices
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