A Damage-Driven Model for Duchenne Muscular Dystrophy: Early-Stage Dynamics and Invasion Thresholds

TL;DR

This paper develops a spatially extended mathematical model for Duchenne muscular dystrophy, analyzing early-stage dynamics, invasion thresholds, and the minimal speed of disease spread, supported by numerical simulations.

Contribution

It introduces a novel damage-driven reaction-diffusion-chemotaxis model and characterizes invasion conditions and propagation speeds for disease progression.

Findings

Diffusion does not cause spatial heterogeneity or Turing patterns.

Disease progression occurs through invasion, not pattern formation.

Explicit conditions for invasion onset and minimal propagation speed are derived.

Abstract

We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis system describing the interaction between healthy tissue, damaged fibers, immune cells and inflammatory signals. We establish the global well-posedness of the system and investigate the early-stage dynamics through linearization around the healthy equilibrium. Our analysis shows that diffusion does not induce Turing instabilities, so that spatial heterogeneity cannot arise from diffusion-driven mechanisms. Instead, disease progression occurs through invasion processes. We derive explicit conditions for the onset of invasion, interpreted as an effective damage reproduction threshold and characterize the minimal propagation speed of pathological fronts, showing that the dynamics is governed by a pulled-front mechanism. Numerical simulations support the analytical results and confirm the transition between decay and invasion. These results provide a mathematical framework for early-stage disease progression and indicate that spatial spreading arise from the expansion of localized damage rather than from intrinsic pattern-forming mechanisms.