An eco-epidemiological predator-prey model where predators distinguish between susceptible and infected prey

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6 Citations (Scopus)

Abstract

A predator-prey model with disease amongst the prey and ratio-dependent functional response for both infected and susceptible prey is proposed and its features analysed. This work is based on previous mathematical models to analyse the important ecosystem of the Salton Sea in Southern California and New Mexico where birds (particularly pelicans) prey on fish (particularly tilapia). The dynamics of the system around each of the ecologically meaningful equilibria are presented. Natural disease control is considered before studying the impact of the disease in the absence of predators, the interaction of predators and healthy prey and the disease effects on predators in the absence of healthy prey. Our theoretical results are confirmed by numerical simulation.
LanguageEnglish
Pages146-166
Number of pages21
JournalMathematical Methods in the Applied Sciences
Volume40
Issue number1
Early online date16 Jun 2016
Publication statusPublished - 15 Jan 2017

Fingerprint

Epidemiological Model
Predator-prey Model
Predator
Prey
Disease control
Birds
Ecosystems
Fish
Ratio-dependent
Functional Response
Mathematical models
Ecosystem
Computer simulation
Mathematical Model
Numerical Simulation
Interaction

Keywords

  • epidemiology
  • ecology
  • differential equations
  • equilibrium
  • stability
  • Hopf bifurcation

Cite this

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title = "An eco-epidemiological predator-prey model where predators distinguish between susceptible and infected prey",
abstract = "A predator-prey model with disease amongst the prey and ratio-dependent functional response for both infected and susceptible prey is proposed and its features analysed. This work is based on previous mathematical models to analyse the important ecosystem of the Salton Sea in Southern California and New Mexico where birds (particularly pelicans) prey on fish (particularly tilapia). The dynamics of the system around each of the ecologically meaningful equilibria are presented. Natural disease control is considered before studying the impact of the disease in the absence of predators, the interaction of predators and healthy prey and the disease effects on predators in the absence of healthy prey. Our theoretical results are confirmed by numerical simulation.",
keywords = "epidemiology , ecology, differential equations , equilibrium, stability, Hopf bifurcation",
author = "David Greenhalgh and Khan, {Qamar J. A.} and Pettigrew, {Joseph S.}",
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KW - ecology

KW - differential equations

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KW - stability

KW - Hopf bifurcation

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