Optimal Control of a Forest Resource Model Under Population Growth and Mining Activities

Asmaidi Asmaidi, Fatmawati Fatmawati, Cicik Alfiniyah

Abstract


Forest resources are essential for maintaining ecological balance and supporting human livelihoods, but population growth and mining expansion have intensified forest degradation. This study develops a nonlinear dynamic model of forest resource management involving forest density, human population, population pressure, and mining activities, and determines optimal intervention strategies for sustainable management. The model is formulated as a four-dimensional system of nonlinear ordinary differential equations with two control variables: environmental education and mining restrictions. The existence of optimal controls is established using the Filippov–Cesari theorem, while Pontryagin’s Maximum Principle is applied to characterize the optimal solutions. Numerical simulations using the forward–backward sweep method show that environmental education reduces population pressure by 9.57%, whereas mining restrictions reduce mining activities by 81.23% and increase forest density by 70.41%. Simultaneous implementation of both controls provides the best outcome, improving forest sustainability while balancing ecological conservation and socioeconomic development objectives.


Keywords


Dynamic model, forest resources; mining activities; optimal control; population pressure

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DOI: https://doi.org/10.18860/cauchy.v11i2.44782

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