Modeling the effect of budget allocation on the abatement of atmospheric carbon dioxide

An increment in carbon dioxide (CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document}) results in global warming posed a threat to the mankind. Mitigation of anthropogenic CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document} emission is important for climate change alleviation. In this regard, some significant steps are taken by the government of every country, which requires budget. In this paper, to observe the effect of budget allocation on the abatement of atmospheric concentration of CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document}, a non-linear mathematical model is formulated and analyzed. In the modeling process, it is considered that a part of the available budget is used for the control of anthropogenic emission and the remaining part of budget is used for afforestation and reforestation. For the proposed model, feasibility and stability of all the equilibria have been discussed. From the model analysis, we have derived that how much budget one should spend on controlling the anthropogenic emission of CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document} and afforestation/reforestation. Furthermore, numerical simulation has been performed to support analytical findings. It has been shown that the atmospheric level of CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document} can be reduced to an innocuous level if the efficacy of allocated budget to control the anthropogenic emission of CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$CO _2$$\end{document} and afforestation/reforestation increases. Moreover, it is found that the growth rate of budget allocation due to an increase in atmospheric level of carbon dioxide may cause stability switch through Hopf-bifurcation.