A Mathematical Model for a Feedback of Stress Responsive Hormones Crh/avp in Hpa Axis Due to Human Stress

Given that a unit is of age ‘t’ the remaining life after time t is random. It is well known that the class of distribution with decreasing mean residual life (DMR), contains the class of distribution with increasing hazard rate. If exponential length-biased approximations, bounds and stability results on the distance between residual life reliability functions, with monotone weight functions and exponential counterpart in the class of distribution functions with increasing or decreasing hazard rate functions are established. In the applications part biologically available cortisol feeds back on hypothalamic CRH/AVP and pituitary ACTH outputs by way of both delayed (time-integrated) and rapid (ratesensitive) inhibitory mechanisms. We incorporate these dynamic relationships in a core biostatistical construct of coupled integral differential equations along with biological variability.