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A Theoretical Approach on Controlling Agricultural Pest by Biological Controls

Acta Biotheoretica volume 62, pages 47–67 (2014)Cite this article

Abstract

In this paper we propose and analyze a prey-predator type dynamical system for pest control where prey population is treated as the pest. We consider two classes for the pest namely susceptible pest and infected pest and the predator population is the natural enemy of the pest. We also consider average delay for both the predation rate i.e. predation to the susceptible pest and infected pest. Considering a subsystem of original system in the absence of infection, we analyze the existence of all possible non-negative equilibria and their stability criteria for both the subsystem as well as the original system. We present the conditions for transcritical bifurcation and Hopf bifurcation in the disease free system. The theoretical evaluations are demonstrated through numerical simulations.

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Acknowledgments

The authors are very grateful to the anonymous reviewers and the handling editor for their useful comments and constructive suggestions for the improvement of the manuscript of the present paper. Research of Soovoojeet Jana is financially supported by University Grants Commission, Government of India (F. 11-2/2002 (SA-1) dated 19 August, 2011).

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Affiliations

  1. Department of Mathematics, Shibpur Sri Ramkrishna Vidyalaya, Howrah, 711102, West Bengal, India

    Prasanta Kumar Mondal

  2. Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103, West Bengal, India

    Soovoojeet Jana & T. K. Kar

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  1. Prasanta Kumar Mondal
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  2. Soovoojeet Jana
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  3. T. K. Kar
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Correspondence to Soovoojeet Jana.

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Mondal, P.K., Jana, S. & Kar, T.K. A Theoretical Approach on Controlling Agricultural Pest by Biological Controls. Acta Biotheor 62, 47–67 (2014). https://doi.org/10.1007/s10441-013-9206-4

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  • DOI: https://doi.org/10.1007/s10441-013-9206-4

Keywords

  • Eco-epidemic model
  • Average delay
  • Global stability
  • Hopf bifurcation
  • Transcritical bifurcation