Global And Exponential Stabilization Of A Chemotactic Alopecia Areata Model With Signal-Dependent Diffusion And Sensitivity

The study explores a chemotaxis model for alopecia areata (AA), focusing on the roles of CD4+ T cells, CD8+ T cells, and IFN-γ in immune-mediated hair loss. It finds that classical solutions are globally bounded when CD8+ T cell proliferation is low relative to their death rates, indicating that reduced immune cells can maintain inflammation and contribute to AA's stability. The research identifies conditions for equilibrium stability and instability, showing potential for globally asymptotic stability under specific parameters. Numerical simulations align with these findings, enhancing understanding of AA's spatio-temporal dynamics.