A Mathematical Model for the Effects of Nitrogen and Phosphorus on Algal Blooms

Abstract

The increase of nutrients in lakes typically stimulates the growth of algae in this environment. Therefore, it is important to understand the connection between nutrient concentration and algal biomass to manage the water pollution caused by excessive plant nutrients. It is worth observing that phosphorus and nitrogen are often considered as the principal limiting nutrients for aquatic algal production due to their short supply compared to cellular growth requirements. In freshwaters, phosphorus is the least abundant among the nutrients needed in large quantity by photosynthetic organisms, hence this is the primary nutrient that limits their growth. The purpose of this work is to compare the effects of nitrogen and phosphorus on the growth of algae in lakes. By using a sensitivity analysis technique, we found that the sources of phosphorus provide a greater risk for bloom of algae than that of nitrogen. Therefore, to reduce the occurrence of algal bloom more attention should be paid for the control of phosphorus input into the lake but the inflow of nitrogen cannot be ignored. The existence of a transcritical bifurcation is discussed and its direction is investigated by applying the projection method technique. Further, to make the system more realistic, time delay involved in the conversion of detritus into nutrients is considered. We show that for increasing values of time delay, the system undergoes an Andronov–Hopf-bifurcation. Some simulations are presented to verify the analytical findings. The results of our study can be helpful for the policy makers to mitigate algal blooms from lakes.