Diseased prey predator model with general Holling type interactions

Area of Science:

• Mathematical Biology
• Ecology
• Theoretical Ecology

Background:

• Food chain modeling relies heavily on interaction function selection.
• Existing diseased prey-predator models often use limited Holling type interactions (I, II, III).
• A gap exists in models incorporating general Holling type interactions for diseased prey-predator systems.

Purpose of the Study:

• To develop and analyze a diseased prey-predator model with general Holling type interactions.
• To investigate the stability, permanence, and dynamic behaviors of the proposed model.
• To explore bifurcation scenarios and the potential for disease eradication through parameter selection.

Main Methods:

• Mathematical modeling of a diseased prey-predator system.
• Derivation of local stability conditions for equilibrium points.
• Analysis of system permanence and impermanence conditions.
• Investigation of global stability.
• Bifurcation analysis using the MATCONT package for general Holling parameters and infection rates.

Main Results:

• The model exhibits rich dynamics, including limit cycles, period-2, higher periodic oscillations, and chaotic behavior.
• Permanence and impermanence conditions for the system were established.
• Bifurcation analysis revealed complex scenarios with variations in interaction parameters and infection rates.
• Demonstrated that specific choices of interaction functions can transition a diseased system to a disease-free state.

Conclusions:

• The general Holling type interaction model provides a more realistic framework for food chain dynamics.
• Parameter selection is crucial for controlling ecosystem stability and potentially eliminating disease.
• Findings offer insights for constructing more accurate and predictive ecological models.