A Mathematical Model for Conservation Strategies of Rare Plants in North Sumatra
Abstract
This study develops a nonlinear mathematical model for the conservation of rare plant populations in North Sumatra by incorporating interactions among rare plants, human populations, population pressure, and fire- and toxicant-control activities. The model is formulated as a system of four nonlinear ordinary differential equations and analyzed using positivity, boundedness, equilibrium, and stability theory. The analysis establishes four equilibrium points, including a biologically relevant coexistence equilibrium. Conditions for the existence of this equilibrium are derived, while its local and global asymptotic stability are established using the Routh–Hurwitz criterion and Lyapunov stability theory, respectively. Numerical simulations using illustrative parameter values are performed to support the analytical results and demonstrate the qualitative behavior of the system. The results provide analytical conditions under which rare plant populations can persist despite human pressure and environmental disturbances. This study is theoretical in nature and is not calibrated using ecological field data; therefore, the numerical results are intended to illustrate model dynamics rather than provide site-specific conservation predictions. The proposed framework contributes to the mathematical understanding of conservation dynamics and may serve as a foundation for future data-driven conservation studies.
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DOI: http://dx.doi.org/10.30829/zero.v10i2.29239
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