Venom absorption produces a rapid rise in blood histamine that then clears more slowly — a classic one-compartment pharmacokinetic curve. Patient sensitivity scales the peak amplitude and how far the reaction spreads beyond the sting site.
H(t) = A · (e^(−k_e·t) − e^(−k_a·t)) / norm
epi effect: H(t) *= e^(−k_epi·(t − t_epi)) for t ≥ t_epi
airway% = 100 − sensitivity_gain · H(t)
- k_a — absorption rate: how fast venom/histamine enters the bloodstream after the sting.
- k_e — elimination rate: how fast the body naturally clears histamine.
- Sensitivity — sets the reaction amplitude and whether it stays local or becomes systemic (throat/airway involvement).
- Epinephrine — pharmacologically counteracts the reaction with its own exponential decay term; given early (near the histamine peak's onset) it reverses airway narrowing quickly, given late it still helps but recovery is slower and the airway dips lower first.
Educational purpose only — this model illustrates the shape of the physiological response and why timing of treatment matters. It is not medical advice; always follow real emergency guidance and call emergency services for a genuine reaction.