Permanence and Global Attractivity of a HPA Axis Model Related to Depression

Teerarat Arunrat, Sanoe Koonprasert, Sekson Sirisubtawee

Abstract

In this paper, a non-autonomous system of the HPA axis, i.e., the hypothalamic-pituitary-adrenal axis. The periodic bell-shaped circadian rhythm function is used in the model. The HPA axis regulates the levels of glucocorticoid hormones in the blood. The axis is an endocrine system which is responsible for coping with stress and depression. Non-negativity of solutions of the model is established. Some sufficient conditions for the permanence of the model are obtained by using the comparison theorem. The global attractivity of the model is proved by constructing a Lyapunov function and using the right upper Dini derivative. Some time series solutions and phase portraits of the model are numerically presented to confirm the analytical results.