Energy-related carbon dioxide ( \(\text {CO}_2\) ) emissions have significantly contributed to the increase in atmospheric \(\text {CO}_2\) concentrations. Curbing the carbon dioxide emissions associated with energy generation is crucial for reducing the radiative forcing of carbon dioxide and tackling the climate change issue. The use of renewable energy technologies is one of the most advocated avenues to reduce the carbon footprint of the energy sector. This study presents a mathematical model designed to analyze the influence of renewable energy technologies on the control of atmospheric \(\text {CO}_2\) concentrations. The proposed model consists of a set of nonlinear differential equations that describe the dynamic interplay among the human population, carbon dioxide level, energy use, and renewable energy technologies. An extensive mathematical analysis of the model is presented to delve into the long-term impact of renewable energy technologies on the control of atmospheric \(\text {CO}_2\) levels. The model’s analysis reveals that increasing the adoption rate of renewable energy technologies and improving their efficiency in reducing carbon dioxide emissions contribute to a reduction in the equilibrium \(\text {CO}_2\) levels in Earth’s atmosphere. One of the primary challenges to the widespread implementation of renewable energy technologies is the associated implementation costs. This study identifies optimal control strategies for lowering \(\text {CO}_2\) levels while simultaneously minimizing the expenses linked to the deployment of renewable energy technologies by employing optimal control theory. Furthermore, sensitivity analysis is conducted to illustrate how changes in key parameters affect the system’s dynamics. Numerical simulations confirm the validity of the theoretical conclusions.
