  This study develops a unified model predicting the whole-body response to
endotoxin. We simulate dynamics using differential equations examining the
response to a lipopolysaccharide (LPS) injection. The model tracks pro- and
anti-inflammatory cytokines (TNF-$\alpha$, IL-6, IL-10), concentrations of
corticotropin-releasing hormone (CRH), adrenocorticotropic hormone (ACTH), and
cortisol in the hypothalamic-pituitary-adrenal (HPA) axis. Daily hormonal
variations are integrated into the model by including circadian oscillations
when tracking CRH. Additionally, the model tracks heart rate, blood pressure,
body temperature, and pain perception. Studied quantities function on
timescales ranging from minutes to days. To understand how endotoxin impacts
the body over this vast span of timescales, we examine the response to
variations in LPS administration methods (single dose, repeated dose, and
continuous dose) as well as the timing of the administration and the amount of
endotoxin released into the system. We calibrate the model to literature data
for a 2 ng/kg LPS bolus injection. Results show that LPS administration during
early morning or late evening generates a more pronounced hormonal response.
Most of the LPS effects are eliminated from the body 24 hours after
administration, the main impact of inflammation remains in the system for 48
hours, and repeated dose simulations show that residual effects remain more
than 10 days after the initial injection. We also show that if the LPS
administration method or total dosage is increased, the system response is
amplified, posing a greater risk of hypotension and pyrexia.
