We propose a simplified mathematical model of the hypothalamus-pituitary-thyroid (HPT) axis in an endocrine system. The considered model is a modification of the model proposed by Mukhopadhyay and Bhattacharyya in [10]. Our system of delay differential equations reconstructs the HPT axis in relation to 24h profiles of human in physiological conditions. Homeostatic control of the thyroid-pituitary axis is considered by using...