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Modeling and analysis of a prey–predator system with disease in the prey

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  • Jana, Soovoojeet
  • Kar, T.K.

Abstract

A three dimensional ecoepidemiological model consisting of susceptible prey, infected prey and predator is proposed and analysed in the present work. The parameter delay is introduced in the model system for considering the time taken by a susceptible prey to become infected. Mathematically we analyze the dynamics of the system such as, boundedness of the solutions, existence of non-negative equilibria, local and global stability of interior equilibrium point. Next we choose delay as a bifurcation parameter to examine the existence of the Hopf bifurcation of the system around its interior equilibrium. Moreover we use the normal form method and center manifold theorem to investigate the direction of the Hopf bifurcation and stability of the bifurcating limit cycle. Some numerical simulations are carried out to support the analytical results.

Suggested Citation

  • Jana, Soovoojeet & Kar, T.K., 2013. "Modeling and analysis of a prey–predator system with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 42-53.
    • Handle: RePEc:eee:chsofr:v:47:y:2013:i:c:p:42-53
    DOI: 10.1016/j.chaos.2012.12.002
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    References listed on IDEAS

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    1. Liu, Xiaoming & Liao, Xiaofeng, 2009. "Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 481-490.
    2. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
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    Cited by:

    1. Juneja, Nishant & Agnihotri, Kulbhushan, 2018. "Conservation of a predator species in SIS prey-predator system using optimal taxation policy," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 86-94.
    2. 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.

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