Modeling the Effects of Algal Bloom on Dissolved Oxygen in Eutrophic Water Bodies

Abstract

Algal blooms have a wide variety of detrimental effects on both the aquatic environment and human activities unfortunately, including a decrease in dissolved oxygen levels in water. In this study, a nonlinear mathematical model has been developed to study the effects of algal bloom on the depletion of dissolved oxygen in eutrophic water sources considering nutrient concentrations, density of algal population, detritus, and concentration of dissolved oxygen as variables. The model’s existence and uniqueness, stability at the equilibrium points, and characteristics with respect to state variables have been performed as some parts of analytical solution, whereas the numerical solution has been performed using the Runge–Kutta $4^{\mathrm{t}\mathrm{h}}$ order technique. The findings of this research reveal that an increase in the quantity of nutrients causes an algal bloom, which in turn lowers the equilibrium level of dissolved oxygen. However, higher levels of detritus ( $>$ 4.7 mg/litre) are hazardous to the generation of dissolved oxygen in water systems. Maximum detritus of 1.0 mg/liter is required for fast algal and dissolved oxygen growth in water bodies; beyond that, algal and dissolved oxygen growth rates are lower. Therefore, increasing public awareness is an essential step in controlling this growing issue; failing to do so will result in problems for our water supply, which will in turn pose a danger to our ecosystem.