African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 245

Full Length Research Paper

A stage-structured two species competition model under the effect of disease

Manju Agarwal
  • Manju Agarwal
  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India.
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Vinay Verma
  • Vinay Verma
  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India.
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  •  Accepted: 22 January 2014
  •  Published: 12 February 2014

Abstract

In this paper we study the dynamics of two competing species model, one of the competing species is stage structured and the disease spreads only in the other competing specie. In order to keep the model simple, we present it under the strong assumption that the disease cannot cross the species barrier. Dynamical behaviors such as positivity, roundedness, stability, bifurcation and persistence of the model, are studied analytically using theories of differential equations. Computer simulations are carried out to substantiate the analytical findings. It is noted that the parameters, c the loss rate of population, t the maturation time and f the intraspecific coefficient are the key parameters which we need to control to keep away the mature healthy population from extinction and the infected individuals of the latter species from extinction respectively.

Key words: Competing species, stage structure, disease, stability, permanence, numerical simulation.

Abbreviation

AMS Subject Classification: 34D05, 34D20.