Search Advanced

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 641-656. doi: 10.3934/mbe.2010.7.641
Previous Article Next Article

A mathematical study of a syntrophic relationship of a model of anaerobic digestion process

  • 1.
    UMR Analyses des Systèmes et Biométrie, INRA 02 Place, INRA-INRIA MERE research team, Viala, 34060 Montpellier
  • 2.
    LBE-INRA, UR050, Avenue des Étangs, 11100 Narbonne & INRA-INRIA MERE research team, UMR Analyses des Systèmes et Biométrie, INRA 02 Place Viala, 34060 Montpellier
  • Received: 01 October 2009 Accepted: 29 June 2018 Published: 01 June 2010

  • MSC : Primary: 92B05, 92D25; Secondary: 34A34, 34D23.

  • A mathematical model involving the syntrophic relationship of two major populations of bacteria (acetogens and methanogens), each responsible for a stage of the methane fermentation process is proposed. A detailed qualitative analysis is carried out. The local and global stability analyses of the equilibria are performed. We demonstrate, under general assumptions of monotonicity, relevant from an applied point of view, the global asymptotic stability of a positive equilibrium point which corresponds to the coexistence of acetogenic and methanogenic bacteria.

    Citation: Miled El Hajji, Frédéric Mazenc, Jérôme Harmand. A mathematical study of a syntrophic relationship of a modelof anaerobic digestion process[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 641-656. doi: 10.3934/mbe.2010.7.641

    Related Papers:

    [1] Tewfik Sari, Miled El Hajji, Jérôme Harmand . The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Mathematical Biosciences and Engineering, 2012, 9(3): 627-645. doi: 10.3934/mbe.2012.9.627
    [2] Boumediene Benyahia, Tewfik Sari . Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model. Mathematical Biosciences and Engineering, 2020, 17(5): 5504-5533. doi: 10.3934/mbe.2020296
    [3] Marion Weedermann . Analysis of a model for the effects of an external toxin on anaerobic digestion. Mathematical Biosciences and Engineering, 2012, 9(2): 445-459. doi: 10.3934/mbe.2012.9.445
    [4] Andrés Donoso-Bravo, Pedro Gajardo, Matthieu Sebbah, Diego Vicencio . Comparison of performance in an anaerobic digestion process: one-reactor vs two-reactor configurations. Mathematical Biosciences and Engineering, 2019, 16(4): 2447-2465. doi: 10.3934/mbe.2019122
    [5] Daniele Bernardo Panaro, Andrea Trucchia, Vincenzo Luongo, Maria Rosaria Mattei, Luigi Frunzo . Global sensitivity analysis and uncertainty quantification for a mathematical model of dry anaerobic digestion in plug-flow reactors. Mathematical Biosciences and Engineering, 2024, 21(9): 7139-7164. doi: 10.3934/mbe.2024316
    [6] Amer Hassan Albargi, Miled El Hajji . Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process. Mathematical Biosciences and Engineering, 2023, 20(4): 6591-6611. doi: 10.3934/mbe.2023283
    [7] Jiang Li, Xiaohui Liu, Chunjin Wei . The impact of fear factor and self-defence on the dynamics of predator-prey model with digestion delay. Mathematical Biosciences and Engineering, 2021, 18(5): 5478-5504. doi: 10.3934/mbe.2021277
    [8] Fabiana Russo, Alberto Tenore, Maria Rosaria Mattei, Luigi Frunzo . Multiscale modelling of the start-up process of anammox-based granular reactors. Mathematical Biosciences and Engineering, 2022, 19(10): 10374-10406. doi: 10.3934/mbe.2022486
    [9] Szymon Sobieszek, Matthew J. Wade, Gail S. K. Wolkowicz . Rich dynamics of a three-tiered anaerobic food-web in a chemostat with multiple substrate inflow. Mathematical Biosciences and Engineering, 2020, 17(6): 7045-7073. doi: 10.3934/mbe.2020363
    [10] Tongqian Zhang, Ning Gao, Tengfei Wang, Hongxia Liu, Zhichao Jiang . Global dynamics of a model for treating microorganisms in sewage by periodically adding microbial flocculants. Mathematical Biosciences and Engineering, 2020, 17(1): 179-201. doi: 10.3934/mbe.2020010
  • A mathematical model involving the syntrophic relationship of two major populations of bacteria (acetogens and methanogens), each responsible for a stage of the methane fermentation process is proposed. A detailed qualitative analysis is carried out. The local and global stability analyses of the equilibria are performed. We demonstrate, under general assumptions of monotonicity, relevant from an applied point of view, the global asymptotic stability of a positive equilibrium point which corresponds to the coexistence of acetogenic and methanogenic bacteria.


  • This article has been cited by:

    1. Analysis of a model for the effects of an external toxin on anaerobic digestion, 2012, 9, 1551-0018, 445, 10.3934/mbe.2012.9.445
    2. T. Sari, M.J. Wade, Generalised approach to modelling a three-tiered microbial food-web, 2017, 291, 00255564, 21, 10.1016/j.mbs.2017.07.005
    3. Simon M. Stump, Christopher A. Klausmeier, Competition and coexistence between a syntrophic consortium and a metabolic generalist, and its effect on productivity, 2016, 404, 00225193, 348, 10.1016/j.jtbi.2016.06.019
    4. Miled El Hajji, How can inter-specific interferences explain coexistence or confirm the competitive exclusion principle in a chemostat?, 2018, 11, 1793-5245, 1850111, 10.1142/S1793524518501115
    5. Y. Daoud, N. Abdellatif, T. Sari, J. Harmand, A. Morozov, Steady state analysis of a syntrophic model: the effect of a new input substrate concentration, 2018, 13, 0973-5348, 31, 10.1051/mmnp/2018037
    6. Marion Weedermann, Gail S. K. Wolkowicz, Joanna Sasara, Optimal biogas production in a model for anaerobic digestion, 2015, 81, 0924-090X, 1097, 10.1007/s11071-015-2051-z
    7. Tewfik Sari, Jérôme Harmand, A model of a syntrophic relationship between two microbial species in a chemostat including maintenance, 2016, 275, 00255564, 1, 10.1016/j.mbs.2016.02.008
    8. E.I.P. Volcke, M. Sbarciog, E.J.L. Noldus, B. De Baets, M. Loccufier, Steady state multiplicity of two-step biological conversion systems with general kinetics, 2010, 228, 00255564, 160, 10.1016/j.mbs.2010.09.004
    9. M.J. Wade, R.W. Pattinson, N.G. Parker, J. Dolfing, Emergent behaviour in a chlorophenol-mineralising three-tiered microbial ‘food web’, 2016, 389, 00225193, 171, 10.1016/j.jtbi.2015.10.032
    10. T. Meadows, M. Weedermann, G. S. K. Wolkowicz, Global Analysis of a Simplified Model of Anaerobic Digestion and a New Result for the Chemostat, 2019, 79, 0036-1399, 668, 10.1137/18M1198788
    11. The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat, 2012, 9, 1551-0018, 627, 10.3934/mbe.2012.9.627
    12. Marco Mauri, Jean-Luc Gouzé, Hidde de Jong, Eugenio Cinquemani, Kiran Raosaheb Patil, Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs, 2020, 16, 1553-7358, e1007795, 10.1371/journal.pcbi.1007795
    13. Matthew J. Wade, Not Just Numbers: Mathematical Modelling and Its Contribution to Anaerobic Digestion Processes, 2020, 8, 2227-9717, 888, 10.3390/pr8080888
    14. Marion Weedermann, Gunog Seo, Gail Wolkowicz, Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition, 2013, 7, 1751-3758, 59, 10.1080/17513758.2012.755573
    15. Alma Mašić, Hermann J. Eberl, Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms, 2012, 74, 0092-8240, 1001, 10.1007/s11538-011-9707-8
    16. Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari, Mathematical analysis of a three-tiered food-web in the chemostat, 2020, 0, 1553-524X, 0, 10.3934/dcdsb.2020369
    17. Tahani Mtar, Radhouane Fekih-Salem, Tewfik Sari, Mortality can produce limit cycles in density-dependent models with a predator-prey relationship, 2022, 27, 1531-3492, 7445, 10.3934/dcdsb.2022049
    18. Amer Hassan Albargi, Miled El Hajji, Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process, 2023, 20, 1551-0018, 6591, 10.3934/mbe.2023283
    19. Abdulrahman Ali Alsolami, Miled El Hajji, Mathematical Analysis of a Bacterial Competition in a Continuous Reactor in the Presence of a Virus, 2023, 11, 2227-7390, 883, 10.3390/math11040883
    20. S. Barua, A. Dénes, 2021, Chapter 18, 978-3-030-73240-0, 281, 10.1007/978-3-030-73241-7_18
    21. Tewfik Sari, Boumediene Benyahia, The operating diagram for a two-step anaerobic digestion model, 2021, 105, 0924-090X, 2711, 10.1007/s11071-021-06722-7
    22. Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari, Operating diagrams for a three-tiered microbial food web in the chemostat, 2022, 85, 0303-6812, 10.1007/s00285-022-01812-5
    23. Sarra Nouaoura, Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari, Mathematical Analysis of a Three-Tiered Model of Anaerobic Digestion, 2021, 81, 0036-1399, 1264, 10.1137/20M1353897
    24. Maximiliano Machado-Higuera, Nohora Meneses-Casas, Andres Hernandez, 2021, Lyapunov Stability Analysis of a Two-Step Anaerobic Digestion Model, 978-1-6654-1883-6, 262, 10.1109/CCAC51819.2021.9633283
    25. Hajji ME, How the competitive exclusion principle can be validated using optical density measurements collected on artificially reconstituted soil ecosystems, 2019, 001, 10.17352/ojeb.000009
    26. Tewfik Sari, Best Operating Conditions for Biogas Production in Some Simple Anaerobic Digestion Models, 2022, 10, 2227-9717, 258, 10.3390/pr10020258
    27. Radhouane Fekih-Salem, Yessmine Daoud, Nahla Abdellatif, Tewfik Sari, A Mathematical Model of Anaerobic Digestion with Syntrophic Relationship, Substrate Inhibition, and Distinct Removal Rates, 2021, 20, 1536-0040, 1621, 10.1137/20M1376480
    28. Nour El Houda Zitouni, Mohamed Dellal, Mustapha Lakrib, Substrate inhibition can produce coexistence and limit cycles in the chemostat model with allelopathy, 2023, 87, 0303-6812, 10.1007/s00285-023-01943-3
    29. Amer Hassan Albargi, Miled El Hajji, Bacterial Competition in the Presence of a Virus in a Chemostat, 2023, 11, 2227-7390, 3530, 10.3390/math11163530
    30. Miled El Hajji, Mathematical modeling for anaerobic digestion under the influence of leachate recirculation, 2023, 8, 2473-6988, 30287, 10.3934/math.20231547
    31. Tewfik Sari, Commensalism and syntrophy in the chemostat: a unifying graphical approach, 2024, 9, 2473-6988, 18625, 10.3934/math.2024907
    32. Nabil Ben Ali, Nahla Abdellatif, Stability and bifurcations in a model of chemostat with two inter‐connected inhibitions and a negative feedback loop, 2024, 0170-4214, 10.1002/mma.10349
    33. Lin Wang, Linlin Bu, Jianhua Wu, Dynamics of a diffusive model in the anaerobic digestion process, 2025, 142, 10075704, 108523, 10.1016/j.cnsns.2024.108523
  • Reader Comments
  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(3662) PDF downloads(622) Cited by(33)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog