A predator-prey model with disease in the prey species only

David Greenhalgh, Mainul Haque

Research output: Journal PublicationArticlepeer-review

86 Citations (Scopus)

Abstract

A predator-prey model with transmissible disease in the prey species is proposed and analysed. The essential mathematical features are analysed with the help of equilibrium, local and global stability analyses and bifurcation theory. We find four possible equilibria. One is where the populations are extinct. Another is where the disease and predator populations are extinct and we find conditions for global stability of this. A third is where both types of prey exist but no predators. The fourth has all three types of individuals present and we find conditions for limit cycles to arise by Hopf bifurcation. Experimental data simulation and brief discussion conclude the paper.

Original languageEnglish
Pages (from-to)911-929
Number of pages19
JournalMathematical Methods in the Applied Sciences
Volume30
Issue number8
DOIs
Publication statusPublished - 25 May 2007
Externally publishedYes

Keywords

  • Boundedness
  • Eco-epidemiology
  • Global stability
  • Hopf bifurcation
  • Local stability
  • Predator-prey model
  • Simulation

ASJC Scopus subject areas

  • Mathematics (all)
  • Engineering (all)

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