Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling.

Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al., 2015), we here present a mathematical model for AA which incorporates HF cycling and illustrates the anagen phase interruption in AA resulting from an inflammatory autoimmune response against HFs. The model couples a system describing the dynamics of autoreactive immune cells with equations modelling the hair cycle. We illustrate states of health, disease and treatment as well as transitions between them. In addition, we perform parameter sensitivity analysis to assess how different processes, such as proliferation, apoptosis and input from stem cells, impact anagen duration in healthy versus AA-affected HFs. The proposed model may help in evaluating the effectiveness of existing treatments and identifying new potential therapeutic targets.