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Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species

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  • Meihong Qiao
  • Anping Liu
  • Urszula Foryś

Abstract

A diffusive predator-prey system with disease in predator species and no-flux boundary condition is considered. Sufficient conditions which ensure persistence of the system are obtained. Conditions of disease-free ecosystem are also studied. Furthermore, sufficient conditions for global asymptotic stability of the unique positive equilibrium and disease-free equilibrium of the system are derived using the approach of Lyapunov function.

Suggested Citation

  • Meihong Qiao & Anping Liu & Urszula Foryś, 2014. "Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
    • Handle: RePEc:hin:jnljam:236208
    DOI: 10.1155/2014/236208
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