Spatial modeling and dynamics of organic matter biodegradation in the absence or presence of bacterivorous grazing

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.