X(t) – biomass,
S(t) – substrate,
DO(t) – dissolved oxygen,
DOmax – maximum amount of dissolved oxygen,
Xr(t) – recycled biomass,
D(t) – dilution rate (the ratio between the flow rate of the influent and the
volume of the aeration tank),
Sin and DOin – concentrations of dissolved oxygen and of substrate in the
mass of the influent,
Y – biomass yield factor,
α – oxygen transfer rate,
W – aeration rate,
K0 – model constant,
r – the ratio between the re-circulated flow rate and the influent flow rate,
β - the ratio between the waste flow rate and the influent flow rate.