Effects of energy sectors on the emission of carbon dioxide gas and environmental temperature

In this paper, we have proposed a nonlinear mathematical model to study the dynamics of atmospheric carbon dioxide $({\rm{CO}}{{\kern 1pt} _{\rm{2}}})$(CO2) and atmospheric temperature due to energy sectors. Energy sector is a major contributor of atmospheric carbon dioxide. We have studied the effects of energy consumption and human population on ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2 level and temperature. Burning of fossil fuels results in an increase of ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2 level and temperature. To curb the ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2 level and temperature, efficient mitigation options are required. Mitigation options, which reduce emission rate of ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2, energy consumption rate and rate of increase in temperature, are considered in this model. By taking the efficiencies of mitigation options as control variables, the optimality system is derived. Numerical simulations are carried out to validate our analytical findings. The optimal profiles of control variables are plotted for different values of emission rate of ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2, energy consumption rate and rate of increase in temperature. Maximum efficiencies of mitigation options are also plotted against to reduce emission rate of ${\rm{CO}}{{\kern 1pt} _{\rm{2}}}$CO2, energy consumption rate and rate of increase in temperature. It is found that mitigation cost of implementation of mitigation options can be minimized by implementing more efficient mitigation options.