The goal is to formulate a physiologically based minimal integrated model describing the dynamics of the neuro-endocrine Hypothalamic-Pituitary-Adrenal (HPA) axis and its coupling to the innate immune system for humans exposed to an infection. The model is formulated as a system of nonlinear ordinary differential equations with multiple feedbacks.

The HPA axis is an important factor in the body response to stress and is involved in many mental diseases such as depression. A novel model of the HPA axis is presented along with results from the analysis of it such as positivity and existence of an attracting trapping region. The model is calibrated to human data obtained from groups of hypercortisolemic depressed subjects, hypocortisolemic depressed subjects and a control group over 24 hours.

The model of the innate immune system describes an acute inflammatory response provoked by different doses of the endotoxin lipopolysaccharide (LPS). The model depicts various biological properties such as positivity and existence of an attracting trapping region. The model is calibrated to rat data and afterwards adjusted to humans.

Finally, biological reasoning and mathematical modelling is used to formulate an integrated model describing the dynamical coupling of the models of the HPA-axis and the innate immune system for humans. The model is validated on independent human data describing the response of TNF-α, ACTH and cortisol after exposure of endotoxin. Various healthy and unhealthy conditions are simulated and discussed.