A predator–prey model with disease in the prey species only |
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Authors: | David Greenhalgh Mainul Haque |
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Institution: | 1. Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, U.K.;2. Department of Mathematics, Krishnath College, Berhampore, West Bengal 742101, IndiaDepartment of Mathematics, Krishnath College, Berhampore, West Bengal 742101, India=== |
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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. Copyright © 2006 John Wiley & Sons, Ltd. |
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Keywords: | predator– prey model eco‐epidemiology boundedness local stability global stability Hopf bifurcation simulation |
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