Global Behavior of Solutions in a Chemotaxis Model for Alopecia Areata with Signal-Dependent Sensitivity

The paper explores a chemotaxis model for alopecia areata, examining the interactions between immune cells and IFN-γ. It establishes that under conditions of weak signal-dependent sensitivities and high density-dependent death rates, classical solutions are uniformly bounded and globally exist in one and two dimensions. Sparse hairless patches can stabilize into alopecia areata if specific proliferation and death rates are met, with either strong random motion or weak chemotactic effects. The model's positive equilibrium is globally asymptotically stable under certain conditions, with small chemotactic sensitivities relative to diffusion coefficients contributing to stability. The study provides insights into the dynamics of immune cell interactions in alopecia areata.