Modeling and simulations for the mitigation of atmospheric carbon dioxide through forest management programs

The growing global population causes more anthropogenic carbon dioxide $(C{O}_2)$ emissions and raises the need for forest products, which in turn causes deforestation and elevated $C{O}_2$ levels. A rise in the concentration of carbon dioxide in the atmosphere is the major reason for global warming. Carbon dioxide concentrations must be reduced soon to achieve the mitigation of climate change. Forest management programs accommodate a way to manage atmospheric $C{O}_2$ levels. For this purpose, we considered a nonlinear fractional model to analyze the impact of forest management policies on mitigating atmospheric $C{O}_2$ concentration. In this investigation, fractional differential equations were solved by utilizing the Atangana Baleanu Caputo derivative operator. It captures memory effects and shows resilience and efficiency in collecting system dynamics with less processing power. This model consists of four compartments, the concentration of carbon dioxide $\mathcal{C}(t)$, human population $\mathcal{N}(t)$, forest biomass $\mathcal{B}(t)$, and forest management programs $\mathcal{P}(t)$ at any time $t$. The existence and uniqueness of the solution for the fractional model are shown. Physical properties of the solution, non-negativity, and boundedness are also proven. The equilibrium points of the model were computed and further analyzed for local and global asymptotic stability. For the numerical solution of the suggested model, the Atangana-Toufik numerical scheme was employed. The acquired results validate analytical results and show the significance of arbitrary order $\delta$. The effect of deforestation activities and forest management strategies were also analyzed on the dynamics of atmospheric carbon dioxide and forest biomass under the suggested technique. The illustrated results describe that the concentration of $C{O}_2$ can be minimized if deforestation activities are controlled and proper forest management policies are developed and implemented. Furthermore, it is determined that switching to low-carbon energy sources, and developing and implementing more effective mitigation measures will result in a decrease in the mitigation of $C{O}_2$.