title: Time lag model for batch bioreactor simulation accounting the effect of micro-organism mortality.
abstract: In the present work, a generalization of the classical model of Monod accounting the influence of both delayed and instant mortalities on the dynamics of the micro-organism population is proposed. The model was analysed and compared with respect to its quality and applicability for simulation of the cultivation process of micro-organisms. Existence of a unique global positive solution of the Cauchy problem for the proposed model is proved and explicit relations between the decay parameters and the nutrition substrate concentration are obtained. These mathematical results allow us to calculate the nutrient substrate concentration which guarantees that the biomass concentration is maximal for every specific type of taxonomic groups of micro-organisms (bacteria, yeasts).
authors.affiliation: Faculty of Mathematics and Informatics, University of Plovdiv , Plovdiv , Bulgaria.
authors.forename: Andrey
authors.initials: A
authors.lastname: Zahariev
authors.affiliation: Faculty of Mathematics and Informatics, University of Plovdiv , Plovdiv , Bulgaria.
authors.forename: Hristo
authors.initials: H
authors.lastname: Kiskinov
authors.affiliation: Department of Biotechnologies, University of Food Technologies , Plovdiv , Bulgaria.
authors.forename: Angel
authors.initials: A
authors.lastname: Angelov
authors.affiliation: Faculty of Mathematics and Informatics, University of Plovdiv , Plovdiv , Bulgaria.
authors.forename: Stoyan
authors.initials: S
authors.lastname: Zlatev
keywords: Monod model; batch bioreactor; delay equations; dynamics of micro-organism populations; micro-organism cultivation