Monodmodel
The Monod model, also called Monod kinetics, is a mathematical description of microbial growth as a function of substrate concentration. It posits that the specific growth rate mu depends on the concentration of a limiting substrate S according to mu = mu_max S / (K_s + S). In this formulation, mu is the specific growth rate (typically per hour), mu_max is the maximum specific growth rate, S is the limiting substrate concentration, and K_s is the half-saturation constant, the substrate level at which mu equals half of mu_max. The Monod equation is analogous to Michaelis–Menten kinetics for enzyme reactions and is widely used in microbiology and bioprocess engineering to model growth in batch, fed-batch, and continuous cultures.
In a simple batch culture, biomass concentration X grows according to dX/dt = mu X, with mu given
Limitations of the basic Monod model include the assumption of a single limiting substrate, constant mu_max