Mathematical model for abnormalities of HPA axis due to stress associated with analytic univalent functions

Abstract

The main interest of this study is to find the activity of Hypothalamic Pituitary Adrenal axis - HPA due to stress by measuring cortisol level. HPA axis is a major part of the system that controls reaction to stress and the main objective is to observe the response of the system over time due to stress by modeling degradation hazard function \(d(x, t)=g(x) q(t), q(t)\) and \(g(x)\) are non-negative functions of time and degradation measure and finding probability distribution to obtain results regarding Mean and Shape of Mean Residual Life for the above distribution- MRL. Obtaining Mean Residual Life is an important and interesting measure which gives the expected remaining life with the present age \(t\) also comparing the effects of stress by applying Stochastic Dominance. Here we develop two functions \(f_1(z)\) and \(f_2(z)\) by using the class of functions of the form \(f(z)=z+\sum_{n=2}^{\infty} a_n z^n\) which are analytic in the open unit disc \(\mathscr{U}=\{z: z \in \mathrm{C}\) and \(|z|<1\}\) whose coefficients \(a_n\) are considered as Probability density function of degradation measure distribution, for which the subordination property holds. The prominent Psychologist Selye's findings about human stress effects are adopted and the concept of Selye's theory is applied and we give a real application of stress induced cortisol response for women with High Waist to Hip Ratio ( central fat) and with Low Waist to Hip Ratio ( peripheral fat). The concluded results coincide with the medical findings.