A single reaction-diffusion equation for the multifarious eruptions of urticaria
Fig 2
Model assumptions and simulation result.
(A, B) Self-activation and self-inhibition loops of histamine via a mast cell, and the detailed functions of the loops. The example graphs are drawn for γ = 0.008, α1 = 0.4, α2 = 5.0 in model (1). (C) A representative simulation result of the model (1) for wheals and histamine. The parameter is assigned to Table 1 (Set I). The initial condition is shown in the figure at t = 0 for histamine. (D-G) Parameter spaces for wheal development with respect to Pmin are plotted by the color bar. Uniform development is the region where wheals are uniformly developed in the area corresponding to no pattern state. Fine-tuning is the region where wheals developed as very fine dots with diameters less than 3 mm and were widely spread over the area corresponding to eruptions shown in Fig 3. q0, , qμ, qγ, qF, qU are labels of parameter values chosen in the simulation results in (Fig 3A–3F).