Modeling the depletion of dissolved oxygen in a water body located near a city

Abstract

Water bodies located nearby cities are much prone to pollution, especially in the developing countries, where effluents treatment facilities are generally lacking. The main reason for this phenomenon is the increasing population in the cities, and the large number of industries located near them. This leads to generation of huge amounts of domestic and industrial sewage that is discharged into the water bodies, increasing their organic pollutant load and resulting in the depletion of dissolved oxygen. In this paper, we propose a mathematical model for this situation, focusing especially on the resulting quality of the water, determined by the level of dissolved oxygen. The model also accounts for resources needed for the population survival and for the industrial operations. In addition, we describe also the decomposition of organic pollutants by bacteria in the aquatic medium. Feasibility conditions and stability criteria of the system's equilibria are determined analytically. The results show that human population and industries are relevant influential factors responsible for the increase in organic pollutants and the decrease in dissolved oxygen in the water body, in the sense that they may exert a destabilizing effect on the system. The numerical simulations confirm the analytical results. Copyright © 2016 John Wiley & Sons, Ltd.

Human Population Effects on the Ulsoor Lake Fish Survival

“…Here, we report the simulations performed to investigate the system behavior using Matlab vR2016a. The (hypothetical) parameter values are chosen within ranges defined in the existing literature [19,8,20,21,37,17,18,7]. For the set of parameter values given in Table 1, the conditions for the feasibility of the equilibrium E * are satisfied and its components are obtained as N * = 0.81 person/m 2 , T * = 1.74 mg/L, B * = 0.26 cell/L, O * = 1.69 mg/L and F * = 1.05 fish/m 2 .…”

“…The Earth's water supply stays the same in time, but human activities may alter its natural cycle, by contaminating it with chemicals and other substances [4,5]. In this respect, human population, agriculture and industries constitute relevant factors for the increase in organic pollutants and eutrophication, which is even exacerbated in lentic ecosystems such as lakes [6], leading to a decrease in DO, thus exerting an overall destabilizing effect on the aquatic ecosystem [7]. Indeed bacteria and other aquatic micro-organisms use DO to decompose organic pollutants [8], an important step of the ecosystem for functioning.…”

Modeling the Direct and Indirect Effects of Pollutants on the Survival of Fish in Water Bodies

“…4 Industries generate a significant quantity of wastewater which contain organic substances, solids and mineral acids. 27 When heavily polluted sewage or other effluents containing high organic matter are discharged into water bodies, they are broken down by microorganisms, which use up the dissolved oxygen.…”

On a spatiotemporal model for pollutants and dissolved oxygen in a river

“…All these models are linear. For models describing the nonlinear process in water bodies involving interactions of DO with organic pollutants, bacteria, and other biological populations, we refer readers to [6,13,16,18,19], where the models are governed by a set of ODEs and both theoretical and numerical results are obtained. In contrast, works based on PDE models are relatively fewer, especially from a mathematical point of view.…”