Analyzing the Synergistic Effects of Population and Pollution on Forest Resources: A Mathematical Model

The alteration in concentration of atmospheric pollutants is influencing the functionality and growth of forests. Also, the growing human demand for forestry resources is detrimentally affecting the sustainability of these valuable resources. In this study, we present a mathematical model that incorporates the influence of atmospheric pollutants on the intrinsic growth rate of forests, while concurrently addressing the utilization of forestry land by the human population for diverse purposes which diminishes the carrying capacity of forestry resources. We establish sufficient conditions under which all relevant dynamic variables stabilize at their equilibria. Upon scrutinizing the model system, we observe multiple bifurcations concerning certain key parameters. Additionally, numerical simulations have been conducted to corroborate the analytically derived findings. Moreover, we fortify the proposed model through the integration of a time delay in the impact of pollutants on the intrinsic growth rate of forestry resources. Despite the conventional belief that introducing a time delay tends to destabilize systems, our resolute delayed model system showcases that a time delay in the effect of pollutants on intrinsic growth rate of forestry resources can, in fact, stabilize the unstable interior equilibrium.