A Microbial Food Web Dynamics Under the Influence of Leachate Recirculation

Fatema Ahmed Al Najim, Miled El Hajji () and Bader Saad Alshammari
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Fatema Ahmed Al Najim: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Miled El Hajji: Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Bader Saad Alshammari: Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia

Mathematics, 2025, vol. 13, issue 13, 1-27

Abstract: The three-tiered microbial food chain without maintenance under leachate recirculation is the subject of a mathematical seven-dimensional dynamical system that is proposed in this work. This model captures the complex interactions between chlorophenol degraders, phenol degraders, and methanogens in the presence of hydrogen inhibition. The implementation allows for investigation of how hydrogen levels affect the overall system dynamics and phenol production. There is a thorough qualitative analysis provided. A stability analysis of equilibrium points is performed. It is demonstrated that the persistence of the three bacteria is correlated with the existence of the positive equilibrium point, assuming some monotonicity properties on the growth rates. Asymptotic coexistence is satisfied, although periodic orbit possibilities are not ruled out. In order to decrease the amount of organic materials within the reactor, we suggest an optimal strategy on the rate of leachate recirculation in the second stage. Lastly, we offer a few numerical investigations that support and strengthen the theoretical conclusions.

Keywords: microbial food web; chemostat; stability; leachate recirculation; optimal strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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