Biodegradation is a pivotal natural process for elemental recycling and preservation of an ecosystem. Mechanistic modeling of biodegradation has to keep track of chemical elements via stoichiometric theory, under which we propose and analyze a spatial movement model in the absence or presence of bacterivorous grazing. Sensitivity analysis shows that the organic matter degradation rate is most sensitive to the grazer’s death rate when the grazer is present and most sensitive to the bacterial death rate when the grazer is absent. Therefore, these two death rates are chosen as the primary parameters in the conditions of most mathematical theorems. The existence, stability and persistence of solutions are proven by applying linear stability analysis, local and global bifurcation theory, and the abstract persistence theory. Through numerical simulations, we obtain the transient and asymptotic dynamics and explore the effects of all parameters on the organic matter decomposition. Grazers either facilitate biodegradation or has no impact on biodegradation, which resolves the “decomposition–facilitation paradox” in the spatial context.

生物降解是元素循环和生态系统保护的关键自然过程。生物降解的机理模型必须通过化学计量理论来跟踪化学元素，在此基础上，我们提出并分析了不存在或不存在细菌性放牧的空间运动模型。敏感性分析表明，当存在放牧者时，有机物降解率对放牧者的死亡率最敏感，而在不放牧者时，有机物降解率对细菌死亡率最敏感。因此，在大多数数学定理的条件下，选择这两个死亡率作为主要参数。应用线性稳定性分析，局部和全局分叉理论以及抽象的持久性理论，证明了解的存在性，稳定性和持久性。通过数值模拟，我们获得了瞬态和渐近动力学，并探索了所有参数对有机物分解的影响。掠食者要么促进生物降解，要么对生物降解没有影响，这解决了空间背景下的“分解－促进悖论”。