Fermentation kinetics including product and substrate inhibitions plus   biomass death: a mathematical analysis
  Fermentation is generally modelled by kinetic equations giving the time evolutions for biomass, substrate, and product concentrations. Although these equations can be solved analytically in simple cases if substrate/product inhibition and biomass death are included, they are typically solved numerically. We propose an analytical treatment of the kinetic equations --including cell death and an arbitrary number of inhibitions-- in which constant yield needs not be assumed. Equations are solved in phase space, i.e. the biomass concentration is written explicitly as a function of the substrate concentration. 
Mathieu Bouville