Masters Theses


"This work focuses on the logistic growth model, where the Gordon-Schaefer model is considered in continuous time. We view the Gordon-Schaefer model as a bioeconomic equation involved in the fishing business, considering biological rates, carrying capacity, and total marginal costs and revenues. In [25], the authors illustrate the analytical solution of the Schaefer model using the integration by parts method and two theorems. The theorems have many assumptions with many different strategies. Due to the nature of the problem, the optimal control system involves many equations and functions, such as the second root of the equation. We concentrate on Theorem 1, where we re-illustrate it with more details and clarifications. We present the four methods for explaining such an optimal path, where the optimal choice of the four strategies generally depends on the particular applications. Also, we provide the Schaefer model's solution by the Euler-Lagrange equation. This thesis also illustrates the Beverton-Holt model and its solution by the Euler-Lagrange equation. The Beverton-Holt model serves as a classical population model considered in the literature for the discrete-time case of the logistic model"--Abstract, page iii.

Committee Member(s)

Adekpedjou, Akim
Insall, Matt


Mathematics and Statistics

Degree Name

M.S. in Mathematics


Missouri University of Science and Technology

Publication Date

Fall 2022


vii, 58 pages

Note about bibliography

Includes bibliographic references (pages 55-57).


© 2022 Nagham Abbas Al Qubbanchee, All rights reserved.

Document Type

Thesis - Open Access

File Type




Thesis Number

T 12214