Dynamic Behavior of Caputo Fractional-Order Model of Forest Biomass, Human Population, and Atmospheric Carbon Dioxide

Moh. Nurul Huda (Department of Mathematics, Faculty of Sciences, Brawijaya University, Malang 65145, Indonesia & Department of Mathematics, Faculty of Sciences, Mulawarman University, Samarinda 75123, Indonesia)
Agus Suryanto (Department of Mathematics, Faculty of Sciences, Brawijaya University, Malang 65145, Indonesia)
Isnani Darti (Department of Mathematics, Faculty of Sciences, Brawijaya University, Malang 65145, Indonesia)
Muhammad Fakhruddin (Research Center for Computing, National Research and Innovation Agency (BRIN), Bogor 16911, Indonesia)

Communication in Biomathematical Sciences
Vol. 9 No. 1 (2026)

This study aims to analyze the dynamical model of CO2 concentration, human population, and forest biomass. Human activities and land-use changes in forested areas play an important role as the primary contributors to the increase in CO2 emissions, which drive global warming. The inclusion of fractionalorder derivatives is considered to examine the long-term memory effects on the interactions within the CO2 concentration model. Theoretical results such as the existence, uniqueness, positivity, and boundedness of solutions, the local and global stability behavior of equilibrium points, and the existence of a Hopf bifurcation are explored. Furthermore, key parameters, including the deforestation rate and memory order, are investigated to determine their influence on the solution behavior of the CO2 concentration model. A fractionalorder numerical scheme is employed to illustrate various scenarios, validating the theoretical findings. The results show that fractional-order changes affect the dynamic behavior of the model. In addition, increased deforestation rates can increase CO2 concentrations and reduce human population in the long term.