Applied Mathematical Sciences, Vol. 8, 2014, no. 159, 7923 - 7934
HIKARI Ltd, www.m-hikari.com
http://dx.doi.org/10.12988/ams.2014.410792
Stability Analysis and Optimal Harvesting
Policy of Prey-Predator Model with Stage
Structure for Predator
Syamsuddin Toaha, Jeffry Kusuma, Khaeruddin and
Mawardi Bahri
Department of Mathematics
Hasanuddin University, Jln. Perintis Kemerdekaan KM 10
Tamalanrea Makassar, 90245, Indonesia
Copyright © 2014 Syamsuddin Toaha, Jeffry Kusuma, Khaeruddin and Mawardi Bahri. This is
an open access article distributed under the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Abstract
In this paper, we study a prey-predator model with stage structure for predator and
constant harvesting efforts of the prey and predator population. The existence and
stability of interior equilibrium point are analyzed. The maximum profit problem
is solved and optimal harvesting policy of present value of revenue is solved using
Pontryagin’s maximum principle. From the analysis, there exists a critical value
of the efforts that maximizes the profit and the present value of the revenue and
the equilibrium point is also remain stable. Finally, numerical examples are given.
Keywords: Prey-predator, stage structure, harvesting, profit, present value
1 Introduction
The prey-predator population model is one of the most popular models in
mathematical ecology. The prey-predator model has been extended by many authors