Stability analysis of a hypothalamic-pituitary-adrenal axis model with inclusion of glucocorticoid receptor and memory

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.