Uniform persistence in a prey-predator model with a diseased predator

Area of Science:

• Mathematical Biology
• Ecology
• Epidemiology

Background:

• The Rosenzweig-MacArthur model describes predator-prey dynamics.
• Holling type II functional response is common in ecological models.
• Introducing disease into predator populations impacts ecosystem stability.

Purpose of the Study:

• To provide a rigorous theoretical explanation for numerical results on a disease-structured predator-prey model.
• To analyze the stability of a cyclic, locally unstable system with predator disease.
• To derive the disease invasion condition within this ecological framework.

Main Methods:

• Utilizing a well-established mathematical approach to persistence.
• Applying iterative repelling conditions on boundary decomposition.
• Conducting a full stability analysis of the model.

Main Results:

• A rigorous theoretical explanation for numerical findings in a predator-prey model with predator disease.
• Demonstration of how the disease invasion condition is derived.
• Identification of conditions leading to cyclic instability.

Conclusions:

• The study offers a robust mathematical framework for understanding disease dynamics in predator-prey systems.
• The derived invasion condition is crucial for predicting disease spread.
• Further research can explore variations in functional responses and disease impacts.