Mathematical Modeling and Control of Gas Emissions, Ozone Depletion, and Ecological Sustainability

The paper has re-modeled a nonlinear differential equation to investigate the relationship among human population growth, carbon dioxide accumulation, forest biomass depletion, and ozone-depleting gases. The stability around the equilibrium point of the system is analyzed both locally and globally. The study shows the nature of the stability state characterized by the high pollution rates and loss of the forest resources. In response, control measures are designed to limit emissions and conserve forests, which are formulated and examined in the context of optimal control theory. The Pontryagin maximum principle is used to derive the necessary conditions for optimality, and sensitivity analysis is used to investigate the effect of important parameters. Numerical simulations are performed to verify the outcomes. The study proves that proper intervention strategies are necessary to create a balance between the environment and human well-being.