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Numerical solution of a spatio-temporal predator-prey model with infected prey
Raimund Bürger1, Gerardo Chowell, Elvis Gavilán
1CI²MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
Mathematical Biosciences and Engineering : MBE
|January 25, 2019
Summary
This study introduces a new eco-epidemiological model where predators hunt infected prey, leading to complex spatial patterns in susceptible prey, infected prey, and predator populations. The model reveals how disease dynamics influence predator-prey interactions and spatial distribution.
Area of Science:
- Mathematical Biology
- Ecology
- Epidemiology
Background:
- Predator-prey dynamics and disease spread are critical ecological processes.
- Integrating spatial dynamics into eco-epidemiological models is essential for realistic pattern formation.
- Previous models often lack the combined complexity of disease-driven predation and spatial spread.
Purpose of the Study:
- To formulate a novel spatio-temporal eco-epidemiological model.
- To investigate pattern formation in predator-prey systems where infection influences predation.
- To analyze the interplay between susceptible-infective dynamics, predator-prey interactions, and spatial diffusion.
Main Methods:
- Combined a non-spatial predator-prey model with an SI epidemic model.
- Incorporated predator movement via a non-local convolution of infected prey density.
- Employed a weighted essentially non-oscillatory (WENO) reconstruction and implicit-explicit Runge-Kutta (IMEX-RK) method for numerical solution.
Main Results:
- The model successfully simulates spatio-temporal pattern formation involving susceptible prey, infected prey, and predators.
- Demonstrated that infection-mediated predation drives complex spatial distributions.
- Numerical solutions revealed emergent patterns influenced by diffusion and reaction dynamics.
Conclusions:
- The developed model provides a framework for understanding eco-epidemiological pattern formation.
- Disease-induced changes in prey vulnerability significantly impact predator-prey spatial dynamics.
- The numerical methods used are effective for solving complex spatio-temporal eco-epidemiological systems.
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