  A simplified mathematical model of oral hydrocortisone delivery in adrenal
insufficiency is described; the model is based on three components (gastric
hydrocortisone, free serum cortisol and bound serum cortisol) and is formulated
in terms of linear kinetics, taking into account the dynamics of
glucocorticoid-protein binding. Motivated by the need to optimise cortisol
replacement in the situations of COVID-19 infection, the model is fitted to
recently-published data on 50 mg dosing and earlier data on 10 mg dosing. The
fitted model is used to predict typical responses to standard dosing regimes,
which involve a larger dose in the morning and 1 or 2 smaller doses later in
the day, and the same regimes with doses doubled. In all cases there is a
circadian-like response, with early morning nadir. The model is also used to
consider an alternative dosing strategy based on four equal and equally-spaced
doses of 10, 20 or 30 mg per 24 h, resulting in a more even response resembling
a response to sustained inflammatory stress.
