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Role of transmissible disease in an infected prey-dependent predator -- prey system

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  • Mainul Haque
  • Joydev Chattopadhyay

Abstract

The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator -- prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E 2 . Finally, we have given an example of a real ecological situation with experimental data simulations.

Suggested Citation

  • Mainul Haque & Joydev Chattopadhyay, 2007. "Role of transmissible disease in an infected prey-dependent predator -- prey system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(2), pages 163-178, April.
    • Handle: RePEc:taf:nmcmxx:v:13:y:2007:i:2:p:163-178
    DOI: 10.1080/13873950600682580
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    Cited by:

    1. Sahoo, Banshidhar & Poria, Swarup, 2015. "Effects of allochthonous inputs in the control of infectious disease of prey," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 1-19.
    2. Mukhopadhyay, B. & Bhattacharyya, R., 2009. "Role of predator switching in an eco-epidemiological model with disease in the prey," Ecological Modelling, Elsevier, vol. 220(7), pages 931-939.

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