MATHEMATICAL MODEL FOR THE RESPONSE OF HPA AXIS APPLYING GOMPERTZ - MAKEHAM DISTRIBUTION IN ASSOCIATION WITH ANALYTIC UNIVALENT FUNCTIONS

Abstract

The study here is to find the activity of Hypothalamic Pituitary Adrenal axis - HPA which is a major part of human system which controls reaction to stress by finding Cortisol level and  the objective is to observe the response of the system over time due to stress by applying the Gompertz - Makeham distribution. Here we develop two functions f ₁(z)and  f ₂(z)  by using the class  of analytic univalent functions in the open unit disc whose coefficients  are considered as Probability density function of  the above mentioned distribution,  for which the Subordination  property, Convex and Star likeness  hold.

Current study leads us to a real life application by considering the effects on the response of HPA axis to acute stress. The concluded results coincide with the medical findings.