2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127668Fermentation 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.4 pages, 4 figuresQuantitative MethodsPopulations and Evolutiontext