A Mathematical Model of Anaerobic Digestion with Syntrophic Relationship, Substrate Inhibition, and Distinct Removal Rates

Fekih-Salem, Radhouane; Daoud, Yessmine; Abdellatif, Nahla; Sari, Tewfik

doi:10.1137/20m1376480

Cited by 15 publications

(8 citation statements)

References 51 publications

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“…The values of these biological parameters are provided in Table E. 13. In addition, the construction of the operating diagram is similar for any other specific growth rate satisfying hypothesis (H1).…”

Section: Curvesmentioning

confidence: 98%

Operating diagram of a flocculation model in the chemostat

Fekih-Salem¹,

Sari

2020

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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International audience The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

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Section: Curvesmentioning

confidence: 98%

Operating diagram of a flocculation model in the chemostat

Fekih-Salem¹,

Sari

2020

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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“…Many works have provided a mathematical study of the syntrophic relationship in a two, [3,10,8,16,15,5], or three-step model [20,7,17,12]. Some of them considered specific growth functions such that those of Monod type, Haldane type, or Contois type, see also [9].…”

Section: Introductionmentioning

confidence: 99%

“…In [5], a new input substrate concentration is added to the model and the authors proved, while extending [16], that a new steady-state appears and the qualitative properties of the model are modified. When inhibition of the second biomass is taken into account in the system, the mathematical study of [8] shows the significant impact of substrate inhibition on the behavior of the process and the emergence of bistability regions. In [20], the authors studied a model in which acetogenesis is inhibited by abundance of hydrogen and hydrogenotrophic methanogenesis is inhibited by the high concentration of acetic acid or the high ph-levels.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of stability of a two-species density-dependent model with inhibition

Ali

Abdellatif

2023

Preprint

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In this paper, we study mathematically and numerically a density-dependent model of the anaerobic digestion process with two species and two substrates involving inhibition. This model describes the interactions of a synthetic microbial community in bioprocesses developed for engineering objectives. By a mathematical analysis, involving a large class of growth functions, we prove the existence of a stable steady state, for any initial conditions. The stability study allows us to construct the operating diagrams by determining and plotting the curves that separate the various regions of stability of the different steady states. Mathematics Subject Classification. 34A34, 34D20, 92B05, 92D25

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“…A simple two-step AD model (called AM2) proposed by [6] provides satisfactory prediction of the AD process and demonstrates the ability to reproduce the experimental data and the dynamical behavior. Many papers in the literature have studied the AM2 model (see [4,7,11,14,17,24,25,27,33] and the reference therein).…”

mentioning

confidence: 99%

“…As it was claimed in [28], the operating diagram remains the most useful answer for the analysis of the behavior of the model according to the parameters. This diagram is often performed both in the biological literature [22,27,30,33] and the mathematical literature [1,2,7,8,9,10,13,14,15,16,17,19,23,25,26,32,31].…”

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confidence: 99%

Operating diagrams for a three-tiered microbial food web in the chemostat

et al. 2022

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In this paper, we consider a three-tiered food web model in a chemostat, including chlorophenol, phenol, and hydrogen substrates and their degraders. The model takes into account the three substrate inflowing concentrations, as well as maintenance, that is, decay terms of the species. The operating diagrams give the asymptotic behavior of the model with respect to the four operating parameters, which are the dilution rate and the three inflowing concentrations of the substrates. These diagrams were obtained only numerically in the existing literature. Using the mathematical analysis of this model obtained in our previous studies, we construct the operating diagrams, by plotting the curves that separate their various regions. Hence, the regions of the operating diagrams are constructed analytically and there is no requirement for time-consuming algorithms to generate the plots, as in the numerical method. Moreover, our method reveals behaviors that have not been detected in the previous numerical studies. The growth functions are of Monod form with the inclusion of a product inhibition term. However, our method applies for a large class of growth functions. We construct operating diagrams with and without maintenance showing the role of maintenance on the stability of the system.

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A Mathematical Model of Anaerobic Digestion with Syntrophic Relationship, Substrate Inhibition, and Distinct Removal Rates

Cited by 15 publications

References 51 publications

Operating diagram of a flocculation model in the chemostat

Operating diagram of a flocculation model in the chemostat

Mathematical analysis of stability of a two-species density-dependent model with inhibition

Operating diagrams for a three-tiered microbial food web in the chemostat

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