This paper describes the model development process in detail, including the formulation of equations and parameters based on existing knowledge of hair cycle dynamics and immune system interactions. Various analyses are conducted to gain insights into the behavior of the model. Illustrative simulations are performed to observe the temporal dynamics of the disease progression under different conditions. Sensitivity analysis using eFAST (Extended Fourier Amplitude Sensitivity Test) is employed to identify the most influential parameters affecting the length of the anagen phase in hair follicles affected by alopecia areata. The findings of the study shed light on the complex dynamics of alopecia areata and contribute to a deeper understanding of the disease mechanisms. The model provides a valuable tool for studying autoimmune hair loss diseases and may have implications for the diagnosis and treatment of such conditions. By simulating the immune response and its effects on hair follicles, the model offers insights into potential treatment strategies that can target immune dysregulation. The temporal mathematical model presented in this dissertation provides a comprehensive framework for investigating alopecia areata and understanding its underlying dynamics. The integration of hair cycle dynamics and immune system interactions enhances our knowledge of the disease and opens avenues for future advancements in diagnosis and treatment approaches.
