A Microbial Food Web Dynamics Under the Influence of Leachate Recirculation

• Published in: Mathematics (Basel) Vol. 13; no. 13; p. 2146
• Main Authors: Al Najim, Fatema Ahmed, El Hajji, Miled, Alshammari, Bader Saad
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2025
• Subjects: Alternative energy sources; Bacteria; Biogas; By products; Carbon dioxide; chemostat; Chlorophenol; Dynamical systems; Food chains; Food chains (Ecology); Hydrogen; Landfill; leachate recirculation; Leachates; Mathematical models; Methane; microbial food web; Microorganisms; Municipal solid waste; optimal strategy; Orbits; Organic materials; Phenols; Pollutants; Qualitative analysis; stability; Stability analysis; System dynamics; United States
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math13132146

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.