Mathematical Modelling of Complete and Truncated Dentrification and Dissimilatory Nitrate Reduction to Ammonium (DNRA) in Agricultural Soils

Current agricultural fertilizers add nitrogen in the form of ammonium and nitrate to the soils where different bacteria enabled processes lead to formation of multiple nitrogen containing compounds included in the global nitrogen cycle. A better understanding of those processes can help control the anthropogenic contribution to greenhouse gases released and the nitrogen containing compounds accumulating in the soils and water sources. We analyze mathematical models of denitrifying and dissimilatory nitrate reduction to ammonium (DNRA) bacteria utilizing nitrogen oxides and organic carbon as substrates, first with minimum principle, then with two Monod terms in the bacterial growth formulation. We compare the two models and show how the changes in the model’s structure affect the steady states feasibility and stability boundaries. We show how the system outcomes depend on the initial conditions as well as the bacterial species’ characteristics. Lastly, we explore truncated reactions with the addition of a third species.