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Diseased prey predator model with general Holling type interactions.

Banshidhar Sahoo1, Swarup Poria1

  • 1Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India.

Applied Mathematics and Computation
|April 15, 2020
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Summary

This study introduces a novel diseased prey-predator model using general Holling type interactions. It reveals that specific interaction function choices can lead to disease-free ecosystems and complex dynamics like chaos.

Keywords:
BifurcationDiseaseGeneral HollingHopf pointPermanenceStability

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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.