A model for the effect of density of human population on the depletion of dissolved oxygen in a water body

Abstract

A nonlinear mathematical model to study the effect of density of human population on the depletion of dissolved oxygen in a water body is proposed and analyzed. The proposed model is governed by interactions among five dependent variables, namely density of resource biomass, density of human population, concentration of organic pollutants, density of bacteria and concentration of dissolved oxygen. In the model formulation, it is assumed that density of resource biomass and density of human population follow logistic models with prey--predator type interaction. The model is analyzed using stability theory of differential equations. The analysis of model shows that increase in human population intensify the depletion in concentration of dissolved oxygen in a water body. Numerical simulations are carried out to illustrate analytical findings. © 2014, Springer Science+Business Media Dordrecht.