Mathematical Modeling of Impact of Pollutants on Industries Based on Resource Biomass

Abstract

Depletion of resources such as forestry, minerals etc. and resource-based industries such as wood and paper etc., due to rising pollution, is one of the biggest challenges which the humankind is facing today. In this paper, a mathematical model has been designed to give an insight into the effect of pollutants on natural resources which in turn affects the growth and stability of industries dependent on such biomass. The model is analyzed using stability theory of differential equations. Five dependent variables are considered in the model and some important assumptions are made. Two equilibria are found in the equilibrium analysis and conditions of local and global stability of interior equilibrium are obtained. Numerical simulation is also done to demonstrate the analytical findings. It is found in the study that as we impose an environmental tax on the polluters, the concentration of pollutants in the environment is controlled and the stable equilibrium shifts in such a way that the densities of resource biomass and dependent industries are close to the densities which correspond to the pollution free ecosystem.