MODELING THE EFFECTS OF WOOD AND NON‐WOOD BASED INDUSTRIES ON FORESTRY RESOURCES

Pollution due to the wood and non‐wood based industries is one of the main reasons for the depletion of forestry resources. On the onset of industrial era, the number of industries was less but now it has increased much due to rapid pace of development. Industrialization affects forestry resources in two ways: (i) using raw materials by wood based industries and cut down by non‐wood based industries and (ii) emitting pollutants by wood and non‐wood based industries. In view of this, in this paper, we have proposed and analyzed a mathematical model to assess the effects of wood and non‐wood based industries on the depletion of forestry resources. In the modeling process, it is assumed that wood and non‐wood based industries deplete the forestry resources directly, whereas pollutants emitted by both types of industries decrease the growth rate of forestry resources indirectly. The equilibria are obtained and their stability is discussed. The model analysis reveals that forestry resources decrease due to the growth in wood based industries but the overgrowth in non‐wood based industries and pollutants emitted by them in the environment adversely affect the forestry resources. Numerical simulation is provided to support analytical findings.     

MODELING THE DEPLETION OF A RENEWABLE RESOURCE BY POPULATION AND INDUSTRIALIZATION: EFFECT OF TECHNOLOGY ON ITS CONSERVATION

Abstract In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of a renewable resource by population and industrialization with resource‐dependent migration. The effect of technology on resource conservation is also considered. In the modeling process, four variables are considered, namely, density of a renewable resource, population density, density of industrialization, and technological effort. Both the growth rate and carrying capacity of resource biomass, which follows logistic model, are assumed to be simultaneously depleted by densities of population and industrialization but it is conserved by technological effort. It is further assumed that densities of population and industrialization increase due to increase in the density of renewable resource. The growth rate of technological effort is assumed to be proportional to the difference of carrying capacity of resource biomass and its current density. The model is analyzed by using the stability theory of differential equations and computer simulation. The model analysis shows that the biomass density decreases due to increase in densities of population and industrialization. It decreases further as the resource‐dependent industrial migration increases. But the resource may never become extinct due to population and industrialization, if technological effort is applied appropriately for its conservation.