Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy

TL;DR

This paper develops a mathematical model linking atmospheric CO2, GDP, forest area, and population to analyze their interactions, stability, and control strategies, supported by real data from China and sensitivity analysis.

Contribution

It introduces a novel four-variable mathematical model for CO2 dynamics incorporating economic and environmental factors, with stability and optimal control analysis validated by actual data.

Findings

Model accurately fits China's CO2 data

Sensitivity analysis identifies key parameters affecting CO2 levels

Optimal control strategies effectively regulate atmospheric CO2

Abstract

Climate change and global warming are among the most significant issues that humanity is currently facing, and also among the issues that pose the greatest threats to all mankind. These issues are primarily driven by abnormal increases in greenhouse gas concentrations. Mathematical modeling serves as a powerful approach to analyze the dynamic patterns of atmospheric carbon dioxide. In this paper, we established a mathmetical model with four state variables to investigate the dynamic behavior of the interaction between atmospheric carbon dioxide, GDP, forest area and human population. Relevant theories were employed to analyze the system's boundedness and the stability of equilibrium points. The parameter values were estimated with the help of the actual data in China and numerical fitting was carried out to verify the results of the theoretical analysis. The sensitivity analysis of the compartments with respect to the model parameters was analyzed by using the Partial Rank Correlation Coefficient (PRCC) and the Latin Hypercube Sampling test. Apply the optimal control theory to regulate the atmospheric carbon dioxide level and provide the corresponding numerical fitting. Finally, corresponding discussions and suggestions were put forward with the help of the results of the theoretical analysis and numerical fitting.