  This paper analyzes a four-dimensional model of the
hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the
glucocorticoid receptor in the pituitary. Due to the spatial separation between
the hypothalamus, pituitary and adrenal glands, distributed time delays are
introduced in the mathematical model. The existence of the positive equilibrium
point is proved and a local stability and bifurcation analysis is provided,
considering several types of delay kernels. The fractional-order model with
discrete time delays is also taken into account. Numerical simulations are
provided to illustrate the effectiveness of the theoretical findings.
