Differential Equation Modeling for Sustainable Resource Management: A Steady-State Optimal Harvesting Approach

Authors

• Iordanka N. Panayotova, Christopher Newport UniversityFollow
• Aleksei Talonov, University of Nevada, Las VegasFollow

Publication Date

9-15-2026

Keywords

Mathematical modeling, Steady-State Optimization, Population modeling, Fish harvesting, Decision-making

Disciplines

Applied Mathematics | Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Population Biology | Science and Mathematics Education

Abstract

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary candidate. The constant harvesting effort $\bar{E}$ and its corresponding equilibrium $(\bar{x},\bar{y})$ are determined simultaneously from the state-equilibrium, adjoint, and stationarity conditions.

The resulting framework illustrates how biological interactions and economic parameters, including harvesting price, cost, and discount rate, influence the stationary harvesting effort and the corresponding long-term population levels. The project provides an accessible pathway for introducing students to the connections among differential equations, numerical computation, optimal control, and sustainable resource management.

Recommended Citation

Panayotova, Iordanka N. and Talonov, Aleksei (2026) "Differential Equation Modeling for Sustainable Resource Management: A Steady-State Optimal Harvesting Approach," CODEE Journal: Vol. 20: Iss. 1, Article 4.
Available at: https://scholarship.claremont.edu/codee/vol20/iss1/4

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.