During orthostatic stress, arterial and cardiopulmonary baroreflexes play a key role in maintaining arterial pressure by regulating heart rate. This study, presents a mathematical model that can predict the dynamics of heart rate regulation in response to postural change from sitting to standing. The model uses blood pressure measured in the finger as an input to model heart rate dynamics in response to changes in baroreceptor nerve firing rate, sympathetic and parasympathetic responses, vestibulo-sympathetic reflex, and concentrations of norepinephrine and acetylcholine. We formulate an inverse least squares problem for parameter estimation and successfully demonstrate that our mathematical model can accurately predict heart rate dynamics observed in data obtained from healthy young, healthy elderly, and hypertensive elderly subjects. One of our key findings indicates that to successfully validate our model against clinical data it is necessary to include the vestibulo-sympathetic reflex. Furthermore our model reveals that the transfer between the nerve firing and blood pressure is non-linear and follows a hysteresis curve. In healthy young people, the hysteresis loop is wide, while in healthy and hypertensive elderly people the hysteresis loop shifts to higher blood pressure values and its area is diminished. Finally, for hypertensive elderly people the hysteresis loop is generally not closed indicating that during postural change from sitting to standing baroreflex modulation does not return to steady state during the first minute of standing.