Determining the Impact of Variation of Harvesting Effort on the Qualitative Behaviour of a Coexistence Steady State Solution and Its Stability in Prey-Predetor Fishery Model

Agwu I. A., Inyama S. C., Umana R. A., Omame A., Ukanwoke N., Ofomata A., Mbachu H. I., Udofia E. S. and Uwakwe J. I.
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Agwu I. A.: Department of Mathematics, Abia State Polytechnics, Aba, Abia State, Nigeria
Inyama S. C.: Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
Umana R. A.: Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
Omame A.: Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
Ukanwoke N.: Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
Ofomata A.: Department of Mathematics and Statistics, Federal Polytechnics, Nekede, Owerri, Imo State, Nigeria
Mbachu H. I.: Department of Statistics, Imo State University, Owerri, Imo State, Nigeria
Udofia E. S.: Department of Mathematics and Statistics, Akwa Ibom University, Nigeria
Uwakwe J. I.: Department of Mathematics, Alvan Ikoku Federal College of Education, Owerri, Imo State, Nigeria

Academic Journal of Applied Mathematical Sciences, 2018, vol. 4, issue 10, 119-128

Abstract: In this paper, we consider a prey-predator fishery model in a three –patch aquatic habitat with selective harvesting of predator and prey populations. We attempt to study the qualitative behaviour of stability and co-existence steady state solution in an interaction between prey and predator populations due to variation of the harvesting effort when other model parameters are fixed using the method of numerical simulation. The innovation of this simulation technique has been used to determine the fraction of harvest and un-harvest resource biomass for prey and predator populations. Explicit expressions and values of the maximum sustainable yield (MSY) and the corresponding populations’ level are obtained. Some sort of control is suggested to avoid over exploitation of resource biomass. Graphical solutions of the model are provided.

Keywords: Prey-predator; Co-existence steady state solution; Stability; Aquatic habitat; Harvesting (search for similar items in EconPapers)
Date: 2018
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