Modeling and analysis of the algal bloom in a lake caused by discharge of nutrients

In this paper, a nonlinear model for the algal bloom in a lake caused by excessive flow of nutrients from domestic drainage and water runoff from agricultural fields, is proposed and analyzed. This model considers interactions of cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen in the lake. It is assumed that detritus, which is formed due to death of algae, supplements the cumulative concentration of the nutrients in the water body, using dissolved oxygen in the process. It is shown that the equilibrium level of algal population is highly dependent on the cumulative rate of discharge of inputs of nutrients in the lake and as this cumulative discharge increases the equilibrium level of algal population increases leading to eutrophication. It is also shown that the equilibrium level of dissolved oxygen decreases but that of detritus increases, as the rate of input of cumulative discharge increases. The same results are also found by numerical solution of the model.