Kong Jude D, Salceanu Paul, Wang Hao
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2R3, Canada.
Department of Mathematics, University of Louisiana at Lafayette, 204 Maxim Doucet Hall, Lafayette, LA, 70504, USA.
J Math Biol. 2018 Feb;76(3):609-644. doi: 10.1007/s00285-017-1152-3. Epub 2017 Jun 29.
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.
生物降解，即有机物质被微生物分解的过程，对于环境有机物质的循环至关重要。理解和预测这种生物降解的动态变化越来越受到行业和政府监管机构的关注。由于环境有机物质的变化难以测量，数学模型对于理解和预测有机物质的动态变化至关重要。经验证据表明，食草动物对微生物的捕食活动有助于促进生物降解。在本文中，我们构建并研究了一种基于化学计量学的有机物质分解模型，该模型用于恒化器培养中，并纳入了食草动物的动态变化。我们确定了物种和化学物质均匀持续存在和灭绝的标准。我们的结果表明：（1）如果在唯一的内部稳态下，细菌的人均增长率大于细菌的死亡率和稀释率之和，那么细菌将均匀持续存在；（2）除此之外，如果（a）食草动物的人均增长率大于稀释率和食草动物死亡率之和，并且（b）细菌的死亡率小于某个阈值，那么食草动物将均匀持续存在。如果进料瓶中有足够的资源，这些条件可以同时实现。与微观世界分解模型的结果相反，在恒化器培养中，化学物质总是持续存在。除了在微观世界模型中观察到的跨临界分岔外，我们的恒化器模型还表现出霍普夫分岔和罗森茨韦格的富集悖论现象。我们的敏感性分析表明，促进降解的最有效方法是降低稀释率。
