Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model

In recent decades, the widespread reliance on fossil fuels has grown substantially, leading to a rise in atmospheric carbon dioxide (CO2), which poses a major global concern. In this study, we develop and analyze a novel mathematical model to examine the interactions between atmospheric CO2, human population, and energy demand. The model assumes that human activities and energy production from traditional sources (oil, coal, and gas) contribute to increasing CO2 level, while a shift in energy dependence from traditional to renewable sources (hydro, solar, etc.) occurs as a result of environmental awareness. We derive sufficient conditions for both local and global stability of the system’s interior equilibrium. Numerical simulations demonstrate that when reliance on renewable energy sources is low, the system can exhibit oscillatory dynamics and various bifurcations. However, beyond a critical threshold of renewable energy dependency, the system stabilizes around the interior equilibrium, leading to a reduction in atmospheric CO2. Additionally, an optimal control problem is formulated to reduce atmospheric CO2 level while minimizing the associated implementation costs.