Mathematical modeling of emission and control of carbon dioxide from infrastructure expansion activities

The rise in atmospheric carbon dioxide (${\text{CO}}_2$) concentration has led to a rise in the global average surface temperatures. Deforestation and infrastructure expansion are key contributors to the increase in ${\text{CO}}_2$ level. This study presents a non-linear mathematical model to explore the impact of infrastructure expansion on deforestation and rise in the atmospheric ${\text{CO}}_2$ concentration. The proposed model considers the growth of infrastructure activities, driven by the increasing population, which in turn reduces the carrying capacity of forest biomass. The model is qualitatively analyzed to examine the system’s behavior in long run. It is found that a high growth rate of infrastructure expansion results in lower equilibrium level of forest biomass and higher ${\text{CO}}_2$ concentrations. Moreover, for high population growth driven by infrastructure expansion, exceeding a critical level of infrastructure growth rate can cause the system to lose stability and generation of limit cycle oscillations through a supercritical Hopf-bifurcation. An increase in the growth rate coefficient of human population due to infrastructure expansion activities and deforestation rate can also lead to stability loss of interior equilibrium and existence of limit cycle oscillations in the system via Hopf-bifurcation. It is noticed that for critically high deforestation rate, the system may enter into transcritical bifurcation, resulting in the extinction of forest biomass. The study is extended to derive the strategies to effectively leverage existing mitigation options to reduce ${\text{CO}}_2$ emissions from infrastructure expansion by taking efficiencies of mitigation options to cut the carbon dioxide emission rate and reduce the declination rate of carrying capacity of forest biomass resulting from infrastructure expansion as time-dependent control variables.