A mathematical model of the effect of nitrogen and phosphorus on the growth of blue-green algae population

Some experimental studies have been done related to the prevention of blooms of blue-green algae (BGA), a major cause of water pollution. Adjustment of the content of nitrogen and phosphorus in water has been shown to be useful in the control of blooms. Here we present a mathematical model to describe how nitrogen and phosphorus affect the bloom, persistence, and extinction of BGA in lakes. With rigorous mathematical theories, we have obtained the equilibrium points of BGA population and proved their stability. With precise quantitative formulae, we prove that the bloom and extinction of blue-green algae in lakes follow the law of minimum and the law of tolerance. Our mathematical description provides a different insight how to use nitrogen and phosphorus more effectively in the control and elimination of blue-green algae blooms.