Journal of Mathematical Biology

, Volume 76, Issue 3, pp 609–644 | Cite as

A stoichiometric organic matter decomposition model in a chemostat culture

  • Jude D. KongEmail author
  • Paul Salceanu
  • Hao Wang


Biodegradation, the disintegration of organic matter by microorganism, is essential for the cycling of environmental organic matter. Understanding and predicting the dynamics of this biodegradation have increasingly gained attention from the industries and government regulators. Since changes in environmental organic matter are strenuous to measure, mathematical models are essential in understanding and predicting the dynamics of organic matters. Empirical evidence suggests that grazers’ preying activity on microorganism helps to facilitate biodegradation. In this paper, we formulate and investigate a stoichiometry-based organic matter decomposition model in a chemostat culture that incorporates the dynamics of grazers. We determine the criteria for the uniform persistence and extinction of the species and chemicals. Our results show that (1) if at the unique internal steady state, the per capita growth rate of bacteria is greater than the sum of the bacteria’s death and dilution rates, then the bacteria will persist uniformly; (2) if in addition to this, (a) the grazers’ per capita growth rate is greater than the sum of the dilution rate and grazers’ death rate, and (b) the death rate of bacteria is less than some threshold, then the grazers will persist uniformly. These conditions can be achieved simultaneously if there are sufficient resources in the feed bottle. As opposed to the microcosm decomposition models’ results, in a chemostat culture, chemicals always persist. Besides the transcritical bifurcation observed in microcosm models, our chemostat model exhibits Hopf bifurcation and Rosenzweig’s paradox of enrichment phenomenon. Our sensitivity analysis suggests that the most effective way to facilitate degradation is to decrease the dilution rate.


Biodegradation Organic matter Microorganism Stoichiometry Chemostat Persistence Sensitivity analysis Bifurcation 

Mathematics Subject Classification

34A34 34C23 34D05 34D20 34C60 37M05 37N25 92B05 92D25 92D40 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsUniversity of Louisiana at LafayetteLafayetteUSA

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