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

Author

Listed:
  • 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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:236208
    DOI: 10.1155/2014/236208
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    References listed on IDEAS

    as
    1. Lina Zhang & Shengmao Fu, 2013. "Nonlinear Instability for a Leslie-Gower Predator-Prey Model with Cross Diffusion," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, November.
    2. Zhong Bo Fang & Liru Qiu, 2013. "Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, November.
    3. Zhong Bo Fang & Liru Qiu, 2013. "Global Existence and Uniform Energy Decay Rates for the Semilinear Parabolic Equation with a Memory Term and Mixed Boundary Condition," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Lina Zhang & Shengmao Fu, 2013. "Nonlinear Instability for a Leslie‐Gower Predator‐Prey Model with Cross Diffusion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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