Modeling the role of renewable energy to mitigate the atmospheric level of carbon dioxide along with sustainable development

Abstract

In the past few decades, the use of fossil fuels has increased dramatically due to industrialization in developing nations. The elevation of carbon dioxide (CO2) has become a serious concern for the entire world. Therefore, most countries want to reduce the use of fossil fuels by transitioning to renewable energy sources. In this research work, we formulate a nonlinear mathematical model to study the interplay between atmospheric CO2, human population, and energy production through traditional energy sources (coal, oil, and gas) and renewable energy sources (solar, wind, and hydro). For the model formulation, we consider that the atmospheric level of CO2 increases due to human activities and energy production through traditional energy sources. Additionally, we consider that the dependency of the human population shifts from traditional to renewable sources of energy as the atmospheric level of CO2 increases. Through the model analysis, we have obtained a condition that implies a change in the equilibrium level of CO2 by increasing the deployment rate of renewable energy sources. This condition demonstrates that the atmospheric level of CO2 can be reversed from its current level through sufficient deployment of renewable energy sources. Moreover, for a certain critical value of the growth rate parameter of renewable energy, three interior equilibria may exist. This situation indicates the presence of hysteresis, which implies that the system may undergo discontinuous jumps between different stable steady states. Furthermore, we discuss an optimal control problem to minimize atmospheric CO2, simultaneously minimizing the cost of the considered strategy.