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

This paper examines a chemotaxis model for alopecia areata (AA), focusing on the interactions between CD$ 4^{+} $ T cells, CD$ 8^{+} $ T cells, and interferon-gamma (IFN-$ \gamma $). The study establishes the uniform boundedness and global existence of solutions in one and two dimensions under certain conditions, such as weak signal-dependent sensitivities and high density-dependent death rates. It also explores the globally asymptotic stability and convergence rates of the model's positive equilibrium. The findings suggest that sparse hairless patches can develop and lead to stable AA when specific conditions regarding proliferation rates, death rates, and chemotactic sensitivities are met.