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

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  • David Greenhalgh
  • Mainul Haque
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
JournalMathematical Methods in the Applied Sciences
Issue number8
Early online date20 Nov 2006
Publication statusPublished - 25 May 2007

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