A study of prey-predator relations for mammals

Q. J.A. Khan*, A. F. Ghaleb

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.

Original languageEnglish
Pages (from-to)171-178
Number of pages8
JournalJournal of Theoretical Biology
Issue number2
Publication statusPublished - Jul 21 2003


  • Boundary collocation method
  • Group defence
  • Laplace's equation
  • Nonlinear model
  • Poincaré expansion
  • Predator
  • Prey
  • Radiation condition

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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