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M. R. Myerscough, B. E. Gray, W. L. Hograth and J. Norbury, “An Analysis of an Ordinary Differential Equation Model for a Two-Species Predator-Prey System with Harvesting and Stocking,” Journal of Mathematical Biology, Vol. 30, 1992, pp. 389-401.

has been cited by the following article:

• TITLE: Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment

  AUTHORS: Mellachervu Naga Srinivas, Mantripragada Ananata Satya Srinivas, Kalyan Das, Nurul Huda Gazi

  KEYWORDS: Prey Predator, Stage Structure, Local and Global Stability, Bionomic Equilibrium, Optimal Harvesting, Pontryagin’s Maximum Principle

  JOURNAL NAME: Applied Mathematics, Vol.2 No.11, November 30, 2011

  ABSTRACT: In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.