Optimal Culling and Biocontrol in a Predator-Prey Model.

Area of Science:

• Ecological modeling
• Invasive species management
• Epidemiology

Background:

• Invasive feral cats pose significant threats to native wildlife, particularly on islands.
• Predation by feral cats can lead to the extinction of vulnerable bird populations.
• Integrated pest management strategies are needed to mitigate these impacts.

Purpose of the Study:

• To formulate and analyze optimal control problems for managing invasive predators.
• To investigate novel control strategies involving scalar and time-dependent controls.
• To assess the effectiveness of combined control methods in reducing predator populations.

Main Methods:

• Formulation of an eco-epidemiological model.
• Analytical solutions for optimal control problems.
• Numerical simulations using a forward-backward sweep method.
• Evaluation across diverse ecological scenarios and initial conditions.

Main Results:

• The study provides analytical insights into optimal control strategies for invasive species.
• Numerical simulations demonstrate the effectiveness of different control methods and their combinations.
• The model identifies scenarios where specific control interventions are most impactful.

Conclusions:

• Optimal control strategies are crucial for managing invasive predators like feral cats.
• Combining methods such as culling, trapping, and infection can enhance conservation outcomes.
• This research offers valuable guidance for protecting endangered species from invasive threats.