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This paper analyzes a four-dimensional model of thehypothalamic-pituitary-adrenal (HPA) axis that includes the influence of theglucocorticoid receptor in the pituitary. Due to the spatial separation betweenthe hypothalamus, pituitary and adrenal glands, distributed time delays areintroduced in the mathematical model. The existence of the positive equilibriumpoint is proved and a local stability and bifurcation analysis is provided,considering several types of delay kernels. The fractional-order model withdiscrete time delays is also taken into account. Numerical simulations areprovided to illustrate the effectiveness of the theoretical findings.

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