Mathematical modeling and analysis of the depletion of dissolved oxygen in water bodies

In this paper, a nonlinear mathematical model is proposed to study the depletion of dissolved oxygen in a water body caused by industrial and household discharges of organic matters (pollutants). The problem is formulated as a food chain model by considering various interaction processes (biodegradation and biochemical) involving organic pollutants, bacteria, protozoa, an aquatic population and dissolved oxygen. Using stability theory, it is shown that as the rate of introduction of organic pollutants in a water body increases, the concentration of dissolved oxygen decreases due to various interaction processes. It is found that if the organic pollutants are continuously discharged into water body, the concentration of dissolved oxygen may become negligibly small, thus threatening the survival of aquatic populations. However, by using some effort to control the cumulative discharge of these pollutants into the water body, the concentration of dissolved oxygen can be maintained at a desired level.