# 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.*

Additional contact information

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 â€“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 populationsâ€™ 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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**Persistent link:** https://EconPapers.repec.org/RePEc:arp:ajoams:2018:p:119-128

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