Mathematical models for vehicular carbon dioxide emission

Abstract

The increasing demand for transportation due to a growing global population has led to more vehicles on the road and increased use of fossil fuels, resulting in higher atmospheric carbon dioxide (CO2) levels and contributing to global warming. Thus, adopting sustainable trans portation practices is crucial for achieving climate change goals, specifically the reduction of greenhouse gas emissions to mitigate global warming. This study presents a nonlinear mathe matical model to analyze the dynamics and control of atmospheric CO2 concentration in rela tion to vehicle emissions. The model is qualitatively analyzed to understand long-term system behavior. Model parameters are calibrated using real-world data on world population, eco nomic activities, atmospheric CO2, forest biomass, and vehicle numbers. Results describes the dependence between vehicle CO2 emissions and atmospheric CO2 levels and impact human population decline. Numerical simulations validate analytical findings, and global sensitivity analysis explores the influence of various parameters on CO2 dynamics. An optimal control problem is formulated and solved by using Pontryagin’s principle, establishing optimality con ditions. Solving the problem reveals that reducing vehicle emissions, implementing reforesta tion efforts, adopting green economy practices, and curbing fossil-fueled vehicle production can cut atmosphericCO2 levels by 2.866%. Consequently, addressing climate change linked to increased atmospheric CO2 concentration is achievable through these measures.