Optimization of an integrated feedback control for a pest management predator-prey model

Area of Science:

• Ecology
• Mathematical Biology
• Pest Management

Background:

• Predator-prey dynamics are crucial in ecological systems.
• Pest control often involves complex interactions requiring mathematical modeling.
• Ratio-dependence and pulse control offer advanced strategies for managing pest populations.

Purpose of the Study:

• To establish and analyze a Leslie-Gower predator-prey model incorporating ratio-dependence and state pulse feedback control.
• To investigate the combined effects of chemical pesticide application and beneficial insect supplementation on pest control.
• To determine optimal control strategies for minimizing pest control costs.

Main Methods:

• Utilizing the successor function method and an analogue of the Poincaré criterion to prove the existence, uniqueness, and stability of periodic solutions.
• Analyzing the system's behavior under different equilibrium conditions (stable E* and E0, unstable E*).
• Formulating and solving an optimization problem to find the minimum cost per period for pest control.

Main Results:

• Demonstrated the existence, uniqueness, and asymptotic stability of periodic solutions under specific conditions.
• Verified the existence of limit cycles in the absence of impulse control when the equilibrium E* is unstable.
• Calculated the optimal threshold for pest control, minimizing costs.

Conclusions:

• The developed model effectively integrates ratio-dependence and pulse control for pest management.
• The study provides a theoretical framework for optimizing pest control strategies by balancing chemical and biological methods.
• Numerical simulations confirm the model's feasibility and practical applicability in real-world pest control scenarios.