Control of atmospheric carbon dioxide level through integrated carbon taxation-reforestation policy: a modeling study

Global warming is a serious issue that affects the environment and mankind. The anthropogenic emissions of carbon dioxide, mainly due to fossil fuel burning and deforestation, are among the root cause of global warming. The goal of this work is to present a mathematical model to analyze the long-term impact of an integrated CO2 taxation-reforestation policy on the mitigation of atmospheric CO2 levels. It is assumed that carbon tax is applied to anthropogenic CO2 emissions and a part of the money generated by carbon taxation is invested to accelerate the reforestation programs. The stability theory of differential equations is applied to examine the qualitative behaviour of the system. Lyapunov stability theory is used to derive sufficient conditions under which the atmospheric carbon dioxide level gets stabilized. It is found that an increment in the deforestation rate coefficient above a threshold level leads to stability loss of interior equilibrium and generation of periodic orbits via Hopf-bifurcation. It is found that the amplitude of the oscillation cycles can be dampened on increasing the maximum efficiency of reforestation programs to increase the forest biomass and above a threshold value of the maximum efficiency of reforestation programs, the periodic oscillations die out. It is found that the seasonality in the application of reforestation efforts may lead to the generation of higher periodic solutions above a threshold level of deforestation rate, making it hard to predict and control the atmospheric CO2 level. The conditions for global attractivity of positive periodic solution of the seasonally forced model are discussed. Numerical simulation has been presented to illustrate the theoretical findings.